What is the Least Common Multiple of 75942 and 75960?

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 75942 and 75960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75942 and 75960, than apply into the LCM equation.

GCF(75942,75960) = 18
LCM(75942,75960) = ( 75942 × 75960) / 18
LCM(75942,75960) = 5768554320 / 18
LCM(75942,75960) = 320475240

Least Common Multiple (LCM) of 75942 and 75960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75942 and 75960. First we will calculate the prime factors of 75942 and 75960.

Prime Factorization of 75942

Prime Factorization of 75960

Now multiplying the highest exponent prime factors to calculate the LCM of 75942 and 75960.

LCM(75942,75960) = 2³ × 3² × 4219¹ × 5¹ × 211¹
LCM(75942,75960) = 320475240