What is the Least Common Multiple of 999 and 1008?

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 999 and 1008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 999 and 1008, than apply into the LCM equation.

GCF(999,1008) = 9
LCM(999,1008) = ( 999 × 1008) / 9
LCM(999,1008) = 1006992 / 9
LCM(999,1008) = 111888

Least Common Multiple (LCM) of 999 and 1008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 999 and 1008. First we will calculate the prime factors of 999 and 1008.

Prime Factorization of 999

Prime Factorization of 1008

Now multiplying the highest exponent prime factors to calculate the LCM of 999 and 1008.

LCM(999,1008) = 3³ × 37¹ × 2⁴ × 7¹
LCM(999,1008) = 111888