What is the Least Common Multiple of 756 and 768?

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 756 and 768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 756 and 768, than apply into the LCM equation.

GCF(756,768) = 12
LCM(756,768) = ( 756 × 768) / 12
LCM(756,768) = 580608 / 12
LCM(756,768) = 48384

Least Common Multiple (LCM) of 756 and 768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 756 and 768. First we will calculate the prime factors of 756 and 768.

Prime Factorization of 756

Prime Factorization of 768

Now multiplying the highest exponent prime factors to calculate the LCM of 756 and 768.

LCM(756,768) = 2⁸ × 3³ × 7¹
LCM(756,768) = 48384