What is the Least Common Multiple of 75690 and 75705?

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 75690 and 75705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75690 and 75705, than apply into the LCM equation.

GCF(75690,75705) = 15
LCM(75690,75705) = ( 75690 × 75705) / 15
LCM(75690,75705) = 5730111450 / 15
LCM(75690,75705) = 382007430

Least Common Multiple (LCM) of 75690 and 75705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75690 and 75705. First we will calculate the prime factors of 75690 and 75705.

Prime Factorization of 75690

Prime Factorization of 75705

Now multiplying the highest exponent prime factors to calculate the LCM of 75690 and 75705.

LCM(75690,75705) = 2¹ × 3² × 5¹ × 29² × 7² × 103¹
LCM(75690,75705) = 382007430