What is the Least Common Multiple of 6750 and 6759?

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 6759 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 6759, than apply into the LCM equation.

GCF(6750,6759) = 9
LCM(6750,6759) = ( 6750 × 6759) / 9
LCM(6750,6759) = 45623250 / 9
LCM(6750,6759) = 5069250

Least Common Multiple (LCM) of 6750 and 6759 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6750 and 6759. First we will calculate the prime factors of 6750 and 6759.

Prime Factorization of 6750

Prime Factorization of 6759

Now multiplying the highest exponent prime factors to calculate the LCM of 6750 and 6759.

LCM(6750,6759) = 2¹ × 3³ × 5³ × 751¹
LCM(6750,6759) = 5069250