What is the Least Common Multiple of 57120 and 57138?

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 57120 and 57138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57120 and 57138, than apply into the LCM equation.

GCF(57120,57138) = 6
LCM(57120,57138) = ( 57120 × 57138) / 6
LCM(57120,57138) = 3263722560 / 6
LCM(57120,57138) = 543953760

Least Common Multiple (LCM) of 57120 and 57138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57120 and 57138. First we will calculate the prime factors of 57120 and 57138.

Prime Factorization of 57120

Prime Factorization of 57138

Now multiplying the highest exponent prime factors to calculate the LCM of 57120 and 57138.

LCM(57120,57138) = 2⁵ × 3¹ × 5¹ × 7¹ × 17¹ × 89¹ × 107¹
LCM(57120,57138) = 543953760