What is the Least Common Multiple of 72960 and 72975?

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 72960 and 72975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72960 and 72975, than apply into the LCM equation.

GCF(72960,72975) = 15
LCM(72960,72975) = ( 72960 × 72975) / 15
LCM(72960,72975) = 5324256000 / 15
LCM(72960,72975) = 354950400

Least Common Multiple (LCM) of 72960 and 72975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72960 and 72975. First we will calculate the prime factors of 72960 and 72975.

Prime Factorization of 72960

Prime Factorization of 72975

Now multiplying the highest exponent prime factors to calculate the LCM of 72960 and 72975.

LCM(72960,72975) = 2⁸ × 3¹ × 5² × 19¹ × 7¹ × 139¹
LCM(72960,72975) = 354950400