Find the least common multiple

The least common multiple is the smallest positive whole number that is a multiple of each of two given whole numbers. It represents the first shared value in their lists of multiples and the smallest quantity that can be divided into equal groups of either size; reasoning includes distinguishing a common multiple from the greatest common factor and recognizing when one number is already a multiple of the other. The focus is on pairs of familiar whole numbers, not algebraic or generalized LCM methods.

Detailed Explanation: Find the least common multiple

A multiple is the result of multiplying a whole number by $1, 2, 3,\ldots$ .

To find the least common multiple (LCM) of two numbers:

List the multiples of each number.
Find numbers that appear in both lists.
Choose the smallest positive number they share.

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

List multiples of $6$ :

6,\ 12,\ 18,\ 24,\ 30,\ldots

List multiples of $8$ :

8,\ 16,\ 24,\ 32,\ldots

The first number that appears in both lists is $24$ . Therefore,

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

Check: $24$ can be divided into equal groups of $6$ and into equal groups of $8$ :

24 \div 6=4 \qquad \text{and} \qquad 24 \div 8=3

Remember, the LCM is a shared multiple, not the greatest common factor.

Learn by doing: Find the least common multiple

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Finding Lowest Common Multiple

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