What is the Least Common Multiple of 55125 and 55140?

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 55125 and 55140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 55125 and 55140, than apply into the LCM equation.

GCF(55125,55140) = 15
LCM(55125,55140) = ( 55125 × 55140) / 15
LCM(55125,55140) = 3039592500 / 15
LCM(55125,55140) = 202639500

Least Common Multiple (LCM) of 55125 and 55140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55125 and 55140. First we will calculate the prime factors of 55125 and 55140.

Prime Factorization of 55125

Prime Factorization of 55140

Now multiplying the highest exponent prime factors to calculate the LCM of 55125 and 55140.

LCM(55125,55140) = 3² × 5³ × 7² × 2² × 919¹
LCM(55125,55140) = 202639500