What is the Least Common Multiple of 21696 and 21700?

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 21696 and 21700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21696 and 21700, than apply into the LCM equation.

GCF(21696,21700) = 4
LCM(21696,21700) = ( 21696 × 21700) / 4
LCM(21696,21700) = 470803200 / 4
LCM(21696,21700) = 117700800

Least Common Multiple (LCM) of 21696 and 21700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21696 and 21700. First we will calculate the prime factors of 21696 and 21700.

Prime Factorization of 21696

Prime Factorization of 21700

Now multiplying the highest exponent prime factors to calculate the LCM of 21696 and 21700.

LCM(21696,21700) = 2⁶ × 3¹ × 113¹ × 5² × 7¹ × 31¹
LCM(21696,21700) = 117700800