What is the Least Common Multiple of 67125 and 67140?

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 67125 and 67140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67125 and 67140, than apply into the LCM equation.

GCF(67125,67140) = 15
LCM(67125,67140) = ( 67125 × 67140) / 15
LCM(67125,67140) = 4506772500 / 15
LCM(67125,67140) = 300451500

Least Common Multiple (LCM) of 67125 and 67140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67125 and 67140. First we will calculate the prime factors of 67125 and 67140.

Prime Factorization of 67125

Prime Factorization of 67140

Now multiplying the highest exponent prime factors to calculate the LCM of 67125 and 67140.

LCM(67125,67140) = 3² × 5³ × 179¹ × 2² × 373¹
LCM(67125,67140) = 300451500