What is the Least Common Multiple of 6750 and 6756?

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 6750 and 6756 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6750 and 6756, than apply into the LCM equation.

GCF(6750,6756) = 6
LCM(6750,6756) = ( 6750 × 6756) / 6
LCM(6750,6756) = 45603000 / 6
LCM(6750,6756) = 7600500

Least Common Multiple (LCM) of 6750 and 6756 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6750 and 6756. First we will calculate the prime factors of 6750 and 6756.

Prime Factorization of 6750

Prime Factorization of 6756

Now multiplying the highest exponent prime factors to calculate the LCM of 6750 and 6756.

LCM(6750,6756) = 2² × 3³ × 5³ × 563¹
LCM(6750,6756) = 7600500