The product of two natural numbers is equal to 120. Find the LCM of these numbers if their GCD is 2.

We will use the fact that for any two integers m and n the following relation holds:

m * n = LCM (m, n) * GCD (m, n), where

LCM (m, n) is the least common multiple of m and n, and GCD (m, n) is the greatest common divisor of m and n.

According to the condition of the problem:

m * n = 120,

GCD (m, n) = 2,

therefore, we can formulate the following equation:

120 = LCM (m, n) * 2.

We solve the resulting equation and find the least common multiple of m and n:

LCM (m, n) = 120/2;

LCM (m, n) = 60.

Answer: The least common multiple of these numbers is 60.