What is the Least Common Multiple of 21984 and 21996?

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 21984 and 21996 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21984 and 21996, than apply into the LCM equation.

GCF(21984,21996) = 12
LCM(21984,21996) = ( 21984 × 21996) / 12
LCM(21984,21996) = 483560064 / 12
LCM(21984,21996) = 40296672

Least Common Multiple (LCM) of 21984 and 21996 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21984 and 21996. First we will calculate the prime factors of 21984 and 21996.

Prime Factorization of 21984

Prime Factorization of 21996

Now multiplying the highest exponent prime factors to calculate the LCM of 21984 and 21996.

LCM(21984,21996) = 2⁵ × 3² × 229¹ × 13¹ × 47¹
LCM(21984,21996) = 40296672