What is the Least Common Multiple of 21984 and 21993?

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 21993 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 21993, than apply into the LCM equation.

GCF(21984,21993) = 3
LCM(21984,21993) = ( 21984 × 21993) / 3
LCM(21984,21993) = 483494112 / 3
LCM(21984,21993) = 161164704

Least Common Multiple (LCM) of 21984 and 21993 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21984 and 21993. First we will calculate the prime factors of 21984 and 21993.

Prime Factorization of 21984

Prime Factorization of 21993

Now multiplying the highest exponent prime factors to calculate the LCM of 21984 and 21993.

LCM(21984,21993) = 2⁵ × 3¹ × 229¹ × 7331¹
LCM(21984,21993) = 161164704