What is the Least Common Multiple of 75675 and 75690?

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 75675 and 75690 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75675 and 75690, than apply into the LCM equation.

GCF(75675,75690) = 15
LCM(75675,75690) = ( 75675 × 75690) / 15
LCM(75675,75690) = 5727840750 / 15
LCM(75675,75690) = 381856050

Least Common Multiple (LCM) of 75675 and 75690 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75675 and 75690. First we will calculate the prime factors of 75675 and 75690.

Prime Factorization of 75675

Prime Factorization of 75690

Now multiplying the highest exponent prime factors to calculate the LCM of 75675 and 75690.

LCM(75675,75690) = 3² × 5² × 1009¹ × 2¹ × 29²
LCM(75675,75690) = 381856050