What is the Least Common Multiple of 768 and 784?

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 768 and 784 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 768 and 784, than apply into the LCM equation.

GCF(768,784) = 16
LCM(768,784) = ( 768 × 784) / 16
LCM(768,784) = 602112 / 16
LCM(768,784) = 37632

Least Common Multiple (LCM) of 768 and 784 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 768 and 784. First we will calculate the prime factors of 768 and 784.

Prime Factorization of 768

Prime Factorization of 784

Now multiplying the highest exponent prime factors to calculate the LCM of 768 and 784.

LCM(768,784) = 2⁸ × 3¹ × 7²
LCM(768,784) = 37632