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LCM of 12 and 15

The least common multiple (LCM) of 12 and 15 is 60. Their greatest common factor (GCF) is 3.

LCM60
GCF3
Prime factors of 122^2 × 3
Prime factors of 153 × 5

Prime factorization method

Write each number as a product of primes: 12 = 2^2 × 3 and 15 = 3 × 5. The LCM takes every prime with its highest power, which gives 60. The GCF takes only the shared primes with their lowest power, which gives 3.

Check with the formula

For two numbers, LCM × GCF = a × b. Here 60 × 3 = 180, and 12 × 15 = 180, so the answer is correct.

Multiples of 12 and 15

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96 … Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120 … The first number that appears in both lists is 60.

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Frequently asked questions

What is the LCM of 12 and 15?

The LCM of 12 and 15 is 60. It is the smallest positive number that both 12 and 15 divide into exactly.

What is the GCF of 12 and 15?

The greatest common factor of 12 and 15 is 3. It is the largest number that divides both without a remainder.

How do I find the LCM of 12 and 15 quickly?

Divide the product by the GCF: 12 × 15 = 180, and 180 ÷ 3 = 60.