# The greatest common divisor of two numbers, one of which is 600, is 120

August 31, 2021 | education

| **The greatest common divisor of two numbers, one of which is 600, is 120. The least common multiple of the same numbers is 4800. Find another number.**

1. By the condition of the problem, for natural numbers x1 and x2, x1 = 600, we have:

a) the greatest common divisor (GCD) of numbers x1 and x2 is:

GCD (x1, x2) = 120; (1)

b) the least common multiple (gcd) of x1 and x2 is:

LCM (x1, x2) = 4800. (2)

2. The product of the greatest common divisor and the least common multiple of two numbers is equal to the product of the numbers themselves:

GCD (x1, x2) * LCM (x1, x2) = x1 * x2,

from here we find the second number:

x2 = GCD (x1, x2) * LCM (x1, x2) / x1;

x2 = 120 * 4800/600 = 120 * 8 = 960.

Answer: 960.

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