What is the Least Common Multiple of 1008 and 1022?

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 1008 and 1022 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1008 and 1022, than apply into the LCM equation.

GCF(1008,1022) = 14
LCM(1008,1022) = ( 1008 × 1022) / 14
LCM(1008,1022) = 1030176 / 14
LCM(1008,1022) = 73584

Least Common Multiple (LCM) of 1008 and 1022 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1008 and 1022. First we will calculate the prime factors of 1008 and 1022.

Prime Factorization of 1008

Prime Factorization of 1022

Now multiplying the highest exponent prime factors to calculate the LCM of 1008 and 1022.

LCM(1008,1022) = 2⁴ × 3² × 7¹ × 73¹
LCM(1008,1022) = 73584