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LCM of 12 and 16

The least common multiple (LCM) of 12 and 16 is 48. Their greatest common factor (GCF) is 4.

LCM48
GCF4
Prime factors of 122^2 × 3
Prime factors of 162^4

Prime factorization method

Write each number as a product of primes: 12 = 2^2 × 3 and 16 = 2^4. The LCM takes every prime with its highest power, which gives 48. The GCF takes only the shared primes with their lowest power, which gives 4.

Check with the formula

For two numbers, LCM × GCF = a × b. Here 48 × 4 = 192, and 12 × 16 = 192, so the answer is correct.

Multiples of 12 and 16

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96 … Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128 … The first number that appears in both lists is 48.

Open the LCM & GCF Calculator

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Frequently asked questions

What is the LCM of 12 and 16?

The LCM of 12 and 16 is 48. It is the smallest positive number that both 12 and 16 divide into exactly.

What is the GCF of 12 and 16?

The greatest common factor of 12 and 16 is 4. It is the largest number that divides both without a remainder.

How do I find the LCM of 12 and 16 quickly?

Divide the product by the GCF: 12 × 16 = 192, and 192 ÷ 4 = 48.