What is the Least Common Multiple of 723 and 735?

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 723 and 735 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 723 and 735, than apply into the LCM equation.

GCF(723,735) = 3
LCM(723,735) = ( 723 × 735) / 3
LCM(723,735) = 531405 / 3
LCM(723,735) = 177135

Least Common Multiple (LCM) of 723 and 735 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 723 and 735. First we will calculate the prime factors of 723 and 735.

Prime Factorization of 723

Prime Factorization of 735

Now multiplying the highest exponent prime factors to calculate the LCM of 723 and 735.

LCM(723,735) = 3¹ × 241¹ × 5¹ × 7²
LCM(723,735) = 177135