What is the least common multiple of 14 36 and 28?

Answer 1

Start by factoring each number completely.

14 = 2 × 7

36 = 2 × 2 × 3 × 3

28 = 2 × 2 × 7

Now write each number in exponential form.

14 = 21 × 71

36 = 22 × 32

28 = 22 × 71

Since we are looking for the smallest multiple common to all three of the given numbers, multiply together the largest power of each prime shown.

The largest power of 2 shown is 22.

The largest power of 3 shown is 32.

The largest power of 7 shown is 71.

So, the least common multiple is 22 × 32 × 71 = 252.