What is the Least Common Multiple of 67856 and 67872?

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 67856 and 67872 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67856 and 67872, than apply into the LCM equation.

GCF(67856,67872) = 16
LCM(67856,67872) = ( 67856 × 67872) / 16
LCM(67856,67872) = 4605522432 / 16
LCM(67856,67872) = 287845152

Least Common Multiple (LCM) of 67856 and 67872 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67856 and 67872. First we will calculate the prime factors of 67856 and 67872.

Prime Factorization of 67856

Prime Factorization of 67872

Now multiplying the highest exponent prime factors to calculate the LCM of 67856 and 67872.

LCM(67856,67872) = 2⁵ × 4241¹ × 3¹ × 7¹ × 101¹
LCM(67856,67872) = 287845152