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.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.