Find common multiples

Common multiples are positive whole numbers that occur in the multiples of each of two or more given positive whole numbers—that is, numbers divisible by every given number. The learner can generate and compare sequences of multiples, identify their overlap, and determine the least common multiple when needed, recognizing that common multiples continue indefinitely; this understanding supports equivalent fractions and common denominators without extending to non-integer or abstract algebraic cases.

Detailed Explanation: Find common multiples

A multiple of a number is the result of multiplying it by a positive whole number.

For example, multiples of $4$ are:

4,\ 8,\ 12,\ 16,\ 20,\ 24,\ldots

The dots mean the pattern continues forever.

Example: Find common multiples of $4$ and $6$

Step 1: List multiples of $4$ .

4,\ 8,\ 12,\ 16,\ 20,\ 24,\ 28,\ 32,\ 36,\ldots

Step 2: List multiples of $6$ .

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

Step 3: Find numbers that appear in both lists.

The numbers $12$ , $24$ , and $36$ appear in both lists. Therefore, they are common multiples of $4$ and $6$ .

\boxed{12,\ 24,\ 36,\ldots}

There are infinitely many common multiples. The least common multiple, or LCM, is the smallest common multiple:

\boxed{\text{LCM}(4,6)=12}

You can check that $12$ is divisible by both numbers:

12\div 4=3 \qquad \text{and} \qquad 12\div 6=2

Learn by doing: Find common multiples

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Finding Lowest Common Multiple

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