Question

What is the least common multiple of 14 and 4

Answer 1

Start by setting up a factor tree for 4 and 14.

4 factors as 2 · 2 and 14 factors as 7 · 2.

When finding the least common multiple, we're looking for factors that match up and here we have a pair of 2's that matches up.

So our least common multiple is 2 from the 2's that match up × the the 2 that doesn't match up x the 7 from the 7 that doesn't match up.

So we have 2 × 2 × 7 or 4 × 7 which is 28.

On my whiteboard, I have attached my factor tree.

Answer 2

28

Explanation:

It is often convenient to compute the Least Common Multiple (LCM) as the product of the numbers divided by their greatest common factor. In this case, that would be ...

LCM = (14 × 4)/2 = 28

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As a check, you can do it by looking at the prime factors of these numbers. The LCM will be the product of the unique factors to their highest powers.

14 = 2·7

4 = 2^2

Unique factors are 2 and 7. The highest power of 2 is 2; the highest power of 7 is 1.

LCM = 2^2·7 = 28