What is the Least Common Multiple of 33120 and 33138?

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 33120 and 33138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33120 and 33138, than apply into the LCM equation.

GCF(33120,33138) = 18
LCM(33120,33138) = ( 33120 × 33138) / 18
LCM(33120,33138) = 1097530560 / 18
LCM(33120,33138) = 60973920

Least Common Multiple (LCM) of 33120 and 33138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33120 and 33138. First we will calculate the prime factors of 33120 and 33138.

Prime Factorization of 33120

Prime Factorization of 33138

Now multiplying the highest exponent prime factors to calculate the LCM of 33120 and 33138.

LCM(33120,33138) = 2⁵ × 3² × 5¹ × 23¹ × 7¹ × 263¹
LCM(33120,33138) = 60973920