Find the LCM of Denominators: 3, 5, 12, and 15

Question

Given four denominators, what is their least common multiple?

$\boxed{3}~~~\boxed{5}~~~\boxed{12}~~~\boxed{15}$

To find the least common multiple (LCM) of 3, 5, 12, and 15, we identify their prime factors:

$3 = 3$

$5 = 5$

$12 = 2^2 \times 3$

$15 = 3 \times 5$

The LCM is obtained by taking the highest power of each prime:

$2^2 \times 3 \times 5 = 60$