What is the Least Common Multiple of 75468 and 75480?

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 75468 and 75480 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75468 and 75480, than apply into the LCM equation.

GCF(75468,75480) = 12
LCM(75468,75480) = ( 75468 × 75480) / 12
LCM(75468,75480) = 5696324640 / 12
LCM(75468,75480) = 474693720

Least Common Multiple (LCM) of 75468 and 75480 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75468 and 75480. First we will calculate the prime factors of 75468 and 75480.

Prime Factorization of 75468

Prime Factorization of 75480

Now multiplying the highest exponent prime factors to calculate the LCM of 75468 and 75480.

LCM(75468,75480) = 2³ × 3¹ × 19¹ × 331¹ × 5¹ × 17¹ × 37¹
LCM(75468,75480) = 474693720