What is the Least Common Multiple of 76125 and 76140?

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 76125 and 76140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76125 and 76140, than apply into the LCM equation.

GCF(76125,76140) = 15
LCM(76125,76140) = ( 76125 × 76140) / 15
LCM(76125,76140) = 5796157500 / 15
LCM(76125,76140) = 386410500

Least Common Multiple (LCM) of 76125 and 76140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76125 and 76140. First we will calculate the prime factors of 76125 and 76140.

Prime Factorization of 76125

Prime Factorization of 76140

Now multiplying the highest exponent prime factors to calculate the LCM of 76125 and 76140.

LCM(76125,76140) = 3⁴ × 5³ × 7¹ × 29¹ × 2² × 47¹
LCM(76125,76140) = 386410500