What is the Least Common Multiple of 67664 and 67680?

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 67664 and 67680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67664 and 67680, than apply into the LCM equation.

GCF(67664,67680) = 16
LCM(67664,67680) = ( 67664 × 67680) / 16
LCM(67664,67680) = 4579499520 / 16
LCM(67664,67680) = 286218720

Least Common Multiple (LCM) of 67664 and 67680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67664 and 67680. First we will calculate the prime factors of 67664 and 67680.

Prime Factorization of 67664

Prime Factorization of 67680

Now multiplying the highest exponent prime factors to calculate the LCM of 67664 and 67680.

LCM(67664,67680) = 2⁵ × 4229¹ × 3² × 5¹ × 47¹
LCM(67664,67680) = 286218720