What is the least common multiple of #{8, 12, 16, 3}?

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Answer 1 · 2018-03-10T13:46:29

48

Let's first do prime factorizations:

$8=2^3$

$12=2^2xx3$

$16=2^4$

$3=3$

Now we look for the largest grouping of each prime in the factorizations.

For the number 2, the largest grouping is in 16:

$LCM=2^4xx...$

The other prime factor is 3. We need one of those (since both 12 and 3 only have one):

$LCM=2^4xx3=48$