Least Common Multiple (LCM) calculator
Least Common Multiple (LCM) calculator - finds LCM for up to 10 given numbers and shows process of dividing by primes with the school-like vertical notation.

# Results: factorization step-by-step

Number #1Number #2
3631752
 3618931 2233
 31752158767938396913234411474971 222333377

# Results: podsumowanie

 Detected numbers Numbers you entered without duplicates 36, 31752 LCM Least common multiple (LCM) 31752 LCM prime factors 23 × 34 × 72 GCD Greatest Common Divisor (GCD) 36 GCD prime factors 22 × 32 Are coprime integers no ✗ Other Processing time (performance) 0ms

# Common sense tells

The multiples of number 36 are:
• 36 (1 × 36),
• 72 (2 × 36),
• 108 (3 × 36),
• ...,
• 31644 (879 × 36),
• 31680 (880 × 36),
• 31716 (881 × 36),
• 31752 (882 × 36),
• 31788 (883 × 36),
• etc.
The multiples of number 31752 are:
• 31752 (1 × 31752),
• 63504 (2 × 31752),
• 95256 (3 × 31752),
• 127008 (4 × 31752),
• 158760 (5 × 31752),
• 190512 (6 × 31752),
• 222264 (7 × 31752),
• 254016 (8 × 31752),
• etc.
The least common multiple is 31752.

# Some facts

• Least common multiple (in short: LCM) is the smallest positive integer that is a multiple of two or more numbers. This means also, it can be divided by these numbers without a reminder.
ⓘ Example: Numbers 2 and 3 have LCM of 6 because 6 divides completely by both two and three.
ⓘ Example: Numbers 4 and 10 have LCM of 20 because 20 divides completely by both 4 and 10.
As you can see in the first example, LCM was simply the product (multiplication) of given numbers. However, in the second example is a much smaller number than multiplication.
• Least common multiple is sometimes called lowest common multiple or smallest common multiple
• The least common multiple of the numbers a and b is usually denoted by LCM(a, b) or lcm(a, b).
$\text{LCM}(a, b) = \text{least common multiple of numbers} \left\{a, b\right\}$
• The least common multiple can also be determined for more numbers e.g. LCM(4, 6, 3) is 12 because it is the lowest number, which is divisible by all those three numbers.
$\text{LCM}(a, b, c, ...) = \text{least common multiple of numbers} \left\{a, b, c, ... \right\}$
• The least common multiple is used for operations on fractions, for example, to calculate the common denominator needed when we add or subtract the fractions.
ⓘ Example: We want to add 1/3 to 1/4. The least common multiple of the denominators 3 and 4 is 12 because this number is divided by both of them:
$\text{LCM}(3, 4) = 12$
To add fractions, we convert them to a common denominator being the least common multiple of both denominators of the input fractions:
$\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{1 \times 4}{3 \times 4} + \dfrac{1 \times 3}{4 \times 3} = \dfrac{4}{12} + \dfrac{3}{12} = \dfrac{7}{12}$
• A property similar to LCM is the greatest common divisor (in short: GCD), which is the largest natural number by which all of the given numbers divide.
• If we have GCD for a pair of numbers, we can use it to calculate LCM and vice versa using the following formula. Unfortunately, it works only for a pair of numbers, i.e. it can't be generalized to more than 2 numbers.
$\text{GCD}(a, b) = \dfrac{a \times b} {\text{LCM}(a, b)}$

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