What is the Least Common Multiple of 744 and 756?

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 744 and 756 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 744 and 756, than apply into the LCM equation.

GCF(744,756) = 12
LCM(744,756) = ( 744 × 756) / 12
LCM(744,756) = 562464 / 12
LCM(744,756) = 46872

Least Common Multiple (LCM) of 744 and 756 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 744 and 756. First we will calculate the prime factors of 744 and 756.

Prime Factorization of 744

Prime Factorization of 756

Now multiplying the highest exponent prime factors to calculate the LCM of 744 and 756.

LCM(744,756) = 2³ × 3³ × 31¹ × 7¹
LCM(744,756) = 46872