What is the Least Common Multiple of 51120 and 51135?

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 51120 and 51135 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51120 and 51135, than apply into the LCM equation.

GCF(51120,51135) = 15
LCM(51120,51135) = ( 51120 × 51135) / 15
LCM(51120,51135) = 2614021200 / 15
LCM(51120,51135) = 174268080

Least Common Multiple (LCM) of 51120 and 51135 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51120 and 51135. First we will calculate the prime factors of 51120 and 51135.

Prime Factorization of 51120

Prime Factorization of 51135

Now multiplying the highest exponent prime factors to calculate the LCM of 51120 and 51135.

LCM(51120,51135) = 2⁴ × 3² × 5¹ × 71¹ × 7¹ × 487¹
LCM(51120,51135) = 174268080