Find the greatest common factor and least common multiple of 75 and 90.

Let’s expand the numbers 75 and 90 into prime factors.
Prime factorization of 75:
75 = 5 * 5 * 3.
Prime factorization of 90:
90 = 2 * 5 * 3 * 3.
The greatest common divisor of numbers is the product of the common prime factors of those numbers.
Then GCD (75; 90) = 5 * 3 = 15.
The least common multiple of natural numbers is the product of the expansion of one of the numbers completely and new factors from the other expansion.
Then LCM (75; 90) = 2 * 5 * 3 * 3 * 5 = 90 * 5 = 450.
Answer: LCM (75, 90) = 450; GCD (75, 90) = 15