What is the Least Common Multiple of 30102 and 30120?

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 30102 and 30120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30102 and 30120, than apply into the LCM equation.

GCF(30102,30120) = 6
LCM(30102,30120) = ( 30102 × 30120) / 6
LCM(30102,30120) = 906672240 / 6
LCM(30102,30120) = 151112040

Least Common Multiple (LCM) of 30102 and 30120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30102 and 30120. First we will calculate the prime factors of 30102 and 30120.

Prime Factorization of 30102

Prime Factorization of 30120

Now multiplying the highest exponent prime factors to calculate the LCM of 30102 and 30120.

LCM(30102,30120) = 2³ × 3¹ × 29¹ × 173¹ × 5¹ × 251¹
LCM(30102,30120) = 151112040