What is the Least Common Multiple of 75960 and 75972?

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 75960 and 75972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75960 and 75972, than apply into the LCM equation.

GCF(75960,75972) = 12
LCM(75960,75972) = ( 75960 × 75972) / 12
LCM(75960,75972) = 5770833120 / 12
LCM(75960,75972) = 480902760

Least Common Multiple (LCM) of 75960 and 75972 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75960 and 75972. First we will calculate the prime factors of 75960 and 75972.

Prime Factorization of 75960

Prime Factorization of 75972

Now multiplying the highest exponent prime factors to calculate the LCM of 75960 and 75972.

LCM(75960,75972) = 2³ × 3² × 5¹ × 211¹ × 13¹ × 487¹
LCM(75960,75972) = 480902760