Question

Find the LCM of 8 and 16.

Answer 1

The least common multiple of 8 and 16 is 16.

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Answer 2

LCM stands for least common multiple, and so the LCM of two number is the smallest possible common multiple of the two numbers.

Since 16 is already a multiple of 8 (and since every number is a multiple of itself), the LCM between 8 and 16 is sixteen itself: it is a multiple of 8, it is a multiple of 16, and there couldn't be a smaller one.

Even though this case was trivial, let's do the computation to learn how to do this in general: first of all, you need the prime factorizations of the two numbers:

$8 = 2^3,\quad 16 = 2^4$

The LCM of the two numbers is composed by all the primes appearing in any of the two factorizations. In case a prime appears in both factorizations, we choose the one with higher exponents.

In this case, 2 is the only prime to appear in both factorizations. So, we choose the one with higher exponent, which is 4, and the answer is $2^4=16$, as we already observed.