What is the Least Common Multiple of 67500 and 67510?

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 67500 and 67510 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67500 and 67510, than apply into the LCM equation.

GCF(67500,67510) = 10
LCM(67500,67510) = ( 67500 × 67510) / 10
LCM(67500,67510) = 4556925000 / 10
LCM(67500,67510) = 455692500

Least Common Multiple (LCM) of 67500 and 67510 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67500 and 67510. First we will calculate the prime factors of 67500 and 67510.

Prime Factorization of 67500

Prime Factorization of 67510

Now multiplying the highest exponent prime factors to calculate the LCM of 67500 and 67510.

LCM(67500,67510) = 2² × 3³ × 5⁴ × 43¹ × 157¹
LCM(67500,67510) = 455692500