Common Multiples

Because the prime factorization of 18 is inside of the prime factorization of 252, we know that 18 is a factor of 252.

If we multiply 2 × 3 × 3 = 18 and 2 × 7 = 14, then 252 = 18 × 14. This means that 18 divides evenly into 252 fourteen times, and 252 is a multiple of 18.

When listing the multiples of 18, the fourteenth multiple is 252:

If the prime factorization of number A is inside of the prime factorization of number B, then number A is a factor of number B, and number B is a multiple of number A.

Practice Identifying Multiples

Tap on the numbers that are multiples of () and have as a factor:

Identifying Common Multiples

The number 252 is a common multiple of 18 and 42 because it is a multiple of 18 and 42. The prime factorizations of 18 and 42 are both inside of the prime factorization of 252.

The number 252 is not a common multiple of 24 and 63 because, even though it is a multiple of 63, it is not a multiple of 24. The prime factorization of 24 is not inside of the prime factorization of 252.

Practice Identifying Common Multiples

Tap on the common multiples of:

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Finding the Least Common Multiple (LCM)

While 252 is a common multiple of 18 and 42, it’s not the only one. To find other common multiples, start by listing multiples of 18 and 42:

Because 18 and 42 both have an infinite number of multiples, there are an infinite number of common multiples—but the least common multiple (LCM) is 126.

Instead of listing multiples to find the least common multiple, we can use the prime factorizations of 18 and 42 to find the least common multiple’s prime factorization.

Practice Finding the Least Common Multiple (LCM)

Find the least common multiple of .

Use the keypad to add enough prime factors to fit prime factorizations. If prime factorizations fit with no extra prime factors, the common multiple is the least common multiple.