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Least common multiple

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm(a,0) as 0 for all a, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility.

Example

What is the LCM of 4 and 6?

Multiples of 4 are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...

and the multiples of 6 are:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers that are in both lists:

12, 24, 36, 48, 60, 72, ....

So, from this list of the first few common multiples of the numbers 4 and 6, their least common multiple is 12.

Computing the least common multiple

The following formula reduces the problem of computing the least common multiple to the problem of computing the greatest common divisor (GCD), also known as the greatest common factor:

lcm(a, b) = |a * b| / gcd(a, b)

LCM

A Venn diagram showing the least common multiples of combinations of 2, 3, 4, 5 and 7 (6 is skipped as it is 2 × 3, both of which are already represented).

For example, a card game which requires its cards to be divided equally among up to 5 players requires at least 60 cards, the number at the intersection of the 2, 3, 4 and 5 sets, but not the 7 set.

References

Wikipedia

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Least common multiple
In arithmetic and number theory, the least common multiple,
lowest common multiple, or smallest common multiple of
two integers a and b, usually denoted by LCM(a, b), is
the smallest positive integer that is divisible by
both a and b. Since division of integers by zero is
undefined, this definition has meaning only if a and b are
both different from zero. However, some authors define lcm(a,0)
as 0 for all a, which is the result of taking the lcm
to be the least upper bound in the lattice of divisibility.
Example
What is the LCM of 4 and 6?
Multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...

and the multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers
that are in both lists:
12, 24, 36, 48, 60, 72, ....

So, from this list of the first few common multiples of
the numbers 4 and 6, their least common multiple is 12.
Computing the least common multiple
The following formula reduces the problem of computing the
least common multiple to the problem of computing the greatest
common divisor (GCD), also known as the greatest common factor:
lcm(a, b) = |a * b| / gcd(a, b)

LCM
A Venn diagram showing the least common multiples of
combinations of 2, 3, 4, 5 and 7 (6 is skipped as
it is 2 × 3, both of which are already represented).
For example, a card game which requires its cards to be
divided equally among up to 5 players requires at least 60
cards, the number at the intersection of the 2, 3, 4
and 5 sets, but not the 7 set.
References
Wikipedia

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Least common multiple
In arithmetic and number theory, the least common multiple,
lowest common multiple, or smallest common multiple of
two integers a and b, usually denoted by LCM(a, b), is
the smallest positive integer that is divisible by
both a and b. Since division of integers by zero is
undefined, this definition has meaning only if a and b are
both different from zero. However, some authors define lcm(a,0)
as 0 for all a, which is the result of taking the lcm
to be the least upper bound in the lattice of divisibility.
Example
What is the LCM of 4 and 6?
Multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...

and the multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers
that are in both lists:
12, 24, 36, 48, 60, 72, ....

So, from this list of the first few common multiples of
the numbers 4 and 6, their least common multiple is 12.
Computing the least common multiple
The following formula reduces the problem of computing the
least common multiple to the problem of computing the greatest
common divisor (GCD), also known as the greatest common factor:
lcm(a, b) = |a * b| / gcd(a, b)

LCM
A Venn diagram showing the least common multiples of
combinations of 2, 3, 4, 5 and 7 (6 is skipped as
it is 2 × 3, both of which are already represented).
For example, a card game which requires its cards to be
divided equally among up to 5 players requires at least 60
cards, the number at the intersection of the 2, 3, 4
and 5 sets, but not the 7 set.
References
Wikipedia

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Least common multiple
In arithmetic and number theory, the least common multiple,
lowest common multiple, or smallest common multiple of
two integers a and b, usually denoted by LCM(a, b), is
the smallest positive integer that is divisible by
both a and b. Since division of integers by zero is
undefined, this definition has meaning only if a and b are
both different from zero. However, some authors define lcm(a,0)
as 0 for all a, which is the result of taking the lcm
to be the least upper bound in the lattice of divisibility.
Example
What is the LCM of 4 and 6?
Multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...

and the multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers
that are in both lists:
12, 24, 36, 48, 60, 72, ....

So, from this list of the first few common multiples of
the numbers 4 and 6, their least common multiple is 12.
Computing the least common multiple
The following formula reduces the problem of computing the
least common multiple to the problem of computing the greatest
common divisor (GCD), also known as the greatest common factor:
lcm(a, b) = |a * b| / gcd(a, b)

LCM
A Venn diagram showing the least common multiples of
combinations of 2, 3, 4, 5 and 7 (6 is skipped as
it is 2 × 3, both of which are already represented).
For example, a card game which requires its cards to be
divided equally among up to 5 players requires at least 60
cards, the number at the intersection of the 2, 3, 4
and 5 sets, but not the 7 set.
References
Wikipedia

, 'i');
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var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',
'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',
'ref', 'ref_src', 'source', 'medium', 'campaign'];
function cleanUrl(url) {
try {
var u = new URL(url, window.location.origin);
var changed = false;
trackingParams.forEach(function(p) {
if (u.searchParams.has(p)) {
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})();
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var __re = new RegExp('^' + "youtube\\.com" + '

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Least common multiple
In arithmetic and number theory, the least common multiple,
lowest common multiple, or smallest common multiple of
two integers a and b, usually denoted by LCM(a, b), is
the smallest positive integer that is divisible by
both a and b. Since division of integers by zero is
undefined, this definition has meaning only if a and b are
both different from zero. However, some authors define lcm(a,0)
as 0 for all a, which is the result of taking the lcm
to be the least upper bound in the lattice of divisibility.
Example
What is the LCM of 4 and 6?
Multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...

and the multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers
that are in both lists:
12, 24, 36, 48, 60, 72, ....

So, from this list of the first few common multiples of
the numbers 4 and 6, their least common multiple is 12.
Computing the least common multiple
The following formula reduces the problem of computing the
least common multiple to the problem of computing the greatest
common divisor (GCD), also known as the greatest common factor:
lcm(a, b) = |a * b| / gcd(a, b)

LCM
A Venn diagram showing the least common multiples of
combinations of 2, 3, 4, 5 and 7 (6 is skipped as
it is 2 × 3, both of which are already represented).
For example, a card game which requires its cards to be
divided equally among up to 5 players requires at least 60
cards, the number at the intersection of the 2, 3, 4
and 5 sets, but not the 7 set.
References
Wikipedia

, 'i');
if (__m === '*' || __re.test(location.href)) {
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Least common multiple
In arithmetic and number theory, the least common multiple,
lowest common multiple, or smallest common multiple of
two integers a and b, usually denoted by LCM(a, b), is
the smallest positive integer that is divisible by
both a and b. Since division of integers by zero is
undefined, this definition has meaning only if a and b are
both different from zero. However, some authors define lcm(a,0)
as 0 for all a, which is the result of taking the lcm
to be the least upper bound in the lattice of divisibility.
Example
What is the LCM of 4 and 6?
Multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...

and the multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers
that are in both lists:
12, 24, 36, 48, 60, 72, ....

So, from this list of the first few common multiples of
the numbers 4 and 6, their least common multiple is 12.
Computing the least common multiple
The following formula reduces the problem of computing the
least common multiple to the problem of computing the greatest
common divisor (GCD), also known as the greatest common factor:
lcm(a, b) = |a * b| / gcd(a, b)

LCM
A Venn diagram showing the least common multiples of
combinations of 2, 3, 4, 5 and 7 (6 is skipped as
it is 2 × 3, both of which are already represented).
For example, a card game which requires its cards to be
divided equally among up to 5 players requires at least 60
cards, the number at the intersection of the 2, 3, 4
and 5 sets, but not the 7 set.
References
Wikipedia

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Least common multiple
In arithmetic and number theory, the least common multiple,
lowest common multiple, or smallest common multiple of
two integers a and b, usually denoted by LCM(a, b), is
the smallest positive integer that is divisible by
both a and b. Since division of integers by zero is
undefined, this definition has meaning only if a and b are
both different from zero. However, some authors define lcm(a,0)
as 0 for all a, which is the result of taking the lcm
to be the least upper bound in the lattice of divisibility.
Example
What is the LCM of 4 and 6?
Multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...

and the multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers
that are in both lists:
12, 24, 36, 48, 60, 72, ....

So, from this list of the first few common multiples of
the numbers 4 and 6, their least common multiple is 12.
Computing the least common multiple
The following formula reduces the problem of computing the
least common multiple to the problem of computing the greatest
common divisor (GCD), also known as the greatest common factor:
lcm(a, b) = |a * b| / gcd(a, b)

LCM
A Venn diagram showing the least common multiples of
combinations of 2, 3, 4, 5 and 7 (6 is skipped as
it is 2 × 3, both of which are already represented).
For example, a card game which requires its cards to be
divided equally among up to 5 players requires at least 60
cards, the number at the intersection of the 2, 3, 4
and 5 sets, but not the 7 set.
References
Wikipedia

, 'i');
if (__m === '*' || __re.test(location.href)) {
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var enabled = true;
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filter: invert(1) hue-rotate(180deg) !important;
background: #2d2d44 !important;
border-color: #444 !important;
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::-webkit-scrollbar-thumb { background: #444 !important; }
::-webkit-scrollbar-thumb:hover { background: #555 !important; }
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::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }
';
}
function removeDarkMode() {
var style = document.getElementById('universal-dark-mode-style');
if (style) style.remove();
}
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document.addEventListener('keydown', function(e) {
if (e.altKey && e.shiftKey && e.key === 'D') {
e.preventDefault();
enabled = !enabled;
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applyDarkMode();
console.log('[Universal Dark Mode] Enabled');
} else {
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console.log('[Universal Dark Mode] Disabled');
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});
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var observer = new MutationObserver(function(mutations) {
if (enabled && !document.getElementById('universal-dark-mode-style')) {
applyDarkMode();
}
});
observer.observe(document.head, { childList: true });
console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');
})();
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
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Least common multiple
In arithmetic and number theory, the least common multiple,
lowest common multiple, or smallest common multiple of
two integers a and b, usually denoted by LCM(a, b), is
the smallest positive integer that is divisible by
both a and b. Since division of integers by zero is
undefined, this definition has meaning only if a and b are
both different from zero. However, some authors define lcm(a,0)
as 0 for all a, which is the result of taking the lcm
to be the least upper bound in the lattice of divisibility.
Example
What is the LCM of 4 and 6?
Multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...

and the multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers
that are in both lists:
12, 24, 36, 48, 60, 72, ....

So, from this list of the first few common multiples of
the numbers 4 and 6, their least common multiple is 12.
Computing the least common multiple
The following formula reduces the problem of computing the
least common multiple to the problem of computing the greatest
common divisor (GCD), also known as the greatest common factor:
lcm(a, b) = |a * b| / gcd(a, b)

LCM
A Venn diagram showing the least common multiples of
combinations of 2, 3, 4, 5 and 7 (6 is skipped as
it is 2 × 3, both of which are already represented).
For example, a card game which requires its cards to be
divided equally among up to 5 players requires at least 60
cards, the number at the intersection of the 2, 3, 4
and 5 sets, but not the 7 set.
References
Wikipedia