What is the Least Common Multiple of 18960 and 18975?

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 18960 and 18975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18960 and 18975, than apply into the LCM equation.

GCF(18960,18975) = 15
LCM(18960,18975) = ( 18960 × 18975) / 15
LCM(18960,18975) = 359766000 / 15
LCM(18960,18975) = 23984400

Least Common Multiple (LCM) of 18960 and 18975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18960 and 18975. First we will calculate the prime factors of 18960 and 18975.

Prime Factorization of 18960

Prime Factorization of 18975

Now multiplying the highest exponent prime factors to calculate the LCM of 18960 and 18975.

LCM(18960,18975) = 2⁴ × 3¹ × 5² × 79¹ × 11¹ × 23¹
LCM(18960,18975) = 23984400