What is the Least Common Multiple of 21678 and 21696?

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 21678 and 21696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21678 and 21696, than apply into the LCM equation.

GCF(21678,21696) = 6
LCM(21678,21696) = ( 21678 × 21696) / 6
LCM(21678,21696) = 470325888 / 6
LCM(21678,21696) = 78387648

Least Common Multiple (LCM) of 21678 and 21696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21678 and 21696. First we will calculate the prime factors of 21678 and 21696.

Prime Factorization of 21678

Prime Factorization of 21696

Now multiplying the highest exponent prime factors to calculate the LCM of 21678 and 21696.

LCM(21678,21696) = 2⁶ × 3¹ × 3613¹ × 113¹
LCM(21678,21696) = 78387648