What is the Least Common Multiple of 21993 and 22008?

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 21993 and 22008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21993 and 22008, than apply into the LCM equation.

GCF(21993,22008) = 3
LCM(21993,22008) = ( 21993 × 22008) / 3
LCM(21993,22008) = 484021944 / 3
LCM(21993,22008) = 161340648

Least Common Multiple (LCM) of 21993 and 22008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21993 and 22008. First we will calculate the prime factors of 21993 and 22008.

Prime Factorization of 21993

Prime Factorization of 22008

Now multiplying the highest exponent prime factors to calculate the LCM of 21993 and 22008.

LCM(21993,22008) = 3¹ × 7331¹ × 2³ × 7¹ × 131¹
LCM(21993,22008) = 161340648