Find the least common multiple

The least common multiple (LCM) of two or more positive whole numbers is the smallest positive number that is a multiple of each, identifying the first shared value in their patterns of multiples. It may be found by listing multiples or by using prime factorizations, taking each prime factor with its greatest exponent; it is distinct from the greatest common factor and is not generally the product of the numbers. This scope focuses on manageable whole numbers and common-denominator or repeating-cycle applications, not advanced generalized treatments.

Detailed Explanation: Find the least common multiple

The least common multiple (LCM) is the smallest positive number that is a multiple of two or more numbers.

To find it, list the multiples of each number until you find the first number that appears in every list.

Example: Find the LCM of $6$ and $8$ .

List multiples of $6$ :

6,\ 12,\ 18,\ 24,\ 30,\ 36,\dots

List multiples of $8$ :

8,\ 16,\ 24,\ 32,\ 40,\dots

Find the first number that appears in both lists. The first shared number is $24$ .

Therefore,

\boxed{\operatorname{LCM}(6,8)=24}

Check: $24$ is a multiple of both numbers because $6\times4=24$ and $8\times3=24$ . Since no smaller positive number appears in both lists, $24$ is the least common multiple.

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Finding Lowest Common Multiple

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Find the least common multiple

Detailed Explanation: Find the least common multiple

Learn by doing: Find the least common multiple

Practice with unlimited practice problems

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Finding Lowest Common Multiple