What is the Least Common Multiple of 51120 and 51138?

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 51138 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 51138, than apply into the LCM equation.

GCF(51120,51138) = 18
LCM(51120,51138) = ( 51120 × 51138) / 18
LCM(51120,51138) = 2614174560 / 18
LCM(51120,51138) = 145231920

Least Common Multiple (LCM) of 51120 and 51138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51120 and 51138. First we will calculate the prime factors of 51120 and 51138.

Prime Factorization of 51120

Prime Factorization of 51138

Now multiplying the highest exponent prime factors to calculate the LCM of 51120 and 51138.

LCM(51120,51138) = 2⁴ × 3³ × 5¹ × 71¹ × 947¹
LCM(51120,51138) = 145231920