What is the Least Common Multiple of 735 and 749?

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 749 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 749, than apply into the LCM equation.

GCF(735,749) = 7
LCM(735,749) = ( 735 × 749) / 7
LCM(735,749) = 550515 / 7
LCM(735,749) = 78645

Least Common Multiple (LCM) of 735 and 749 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 735 and 749. First we will calculate the prime factors of 735 and 749.

Prime Factorization of 735

Prime Factorization of 749

Now multiplying the highest exponent prime factors to calculate the LCM of 735 and 749.

LCM(735,749) = 3¹ × 5¹ × 7² × 107¹
LCM(735,749) = 78645