What is the Least Common Multiple of 735 and 750?

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 735 and 750 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 735 and 750, than apply into the LCM equation.

GCF(735,750) = 15
LCM(735,750) = ( 735 × 750) / 15
LCM(735,750) = 551250 / 15
LCM(735,750) = 36750

Least Common Multiple (LCM) of 735 and 750 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 735 and 750. First we will calculate the prime factors of 735 and 750.

Prime Factorization of 735

Prime Factorization of 750

Now multiplying the highest exponent prime factors to calculate the LCM of 735 and 750.

LCM(735,750) = 3¹ × 5³ × 7² × 2¹
LCM(735,750) = 36750