What is the Least Common Multiple of 1020 and 1038?

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 1020 and 1038 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1020 and 1038, than apply into the LCM equation.

GCF(1020,1038) = 6
LCM(1020,1038) = ( 1020 × 1038) / 6
LCM(1020,1038) = 1058760 / 6
LCM(1020,1038) = 176460

Least Common Multiple (LCM) of 1020 and 1038 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1020 and 1038. First we will calculate the prime factors of 1020 and 1038.

Prime Factorization of 1020

Prime Factorization of 1038

Now multiplying the highest exponent prime factors to calculate the LCM of 1020 and 1038.

LCM(1020,1038) = 2² × 3¹ × 5¹ × 17¹ × 173¹
LCM(1020,1038) = 176460