What is the Least Common Multiple of 75084 and 75088?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 75084 and 75088 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75084 and 75088, than apply into the LCM equation.

GCF(75084,75088) = 4
LCM(75084,75088) = ( 75084 × 75088) / 4
LCM(75084,75088) = 5637907392 / 4
LCM(75084,75088) = 1409476848

Least Common Multiple (LCM) of 75084 and 75088 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75084 and 75088. First we will calculate the prime factors of 75084 and 75088.

Prime Factorization of 75084

Prime Factorization of 75088

Now multiplying the highest exponent prime factors to calculate the LCM of 75084 and 75088.

LCM(75084,75088) = 2⁴ × 3¹ × 6257¹ × 13¹ × 19²
LCM(75084,75088) = 1409476848