What is the Least Common Multiple of 30735 and 30744?

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 30735 and 30744 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30735 and 30744, than apply into the LCM equation.

GCF(30735,30744) = 9
LCM(30735,30744) = ( 30735 × 30744) / 9
LCM(30735,30744) = 944916840 / 9
LCM(30735,30744) = 104990760

Least Common Multiple (LCM) of 30735 and 30744 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30735 and 30744. First we will calculate the prime factors of 30735 and 30744.

Prime Factorization of 30735

Prime Factorization of 30744

Now multiplying the highest exponent prime factors to calculate the LCM of 30735 and 30744.

LCM(30735,30744) = 3² × 5¹ × 683¹ × 2³ × 7¹ × 61¹
LCM(30735,30744) = 104990760