What is the Least Common Multiple of 54120 and 54138?

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 54120 and 54138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54120 and 54138, than apply into the LCM equation.

GCF(54120,54138) = 6
LCM(54120,54138) = ( 54120 × 54138) / 6
LCM(54120,54138) = 2929948560 / 6
LCM(54120,54138) = 488324760

Least Common Multiple (LCM) of 54120 and 54138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54120 and 54138. First we will calculate the prime factors of 54120 and 54138.

Prime Factorization of 54120

Prime Factorization of 54138

Now multiplying the highest exponent prime factors to calculate the LCM of 54120 and 54138.

LCM(54120,54138) = 2³ × 3¹ × 5¹ × 11¹ × 41¹ × 7¹ × 1289¹
LCM(54120,54138) = 488324760