What is the Least Common Multiple of 30225 and 30240?

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 30225 and 30240 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30225 and 30240, than apply into the LCM equation.

GCF(30225,30240) = 15
LCM(30225,30240) = ( 30225 × 30240) / 15
LCM(30225,30240) = 914004000 / 15
LCM(30225,30240) = 60933600

Least Common Multiple (LCM) of 30225 and 30240 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30225 and 30240. First we will calculate the prime factors of 30225 and 30240.

Prime Factorization of 30225

Prime Factorization of 30240

Now multiplying the highest exponent prime factors to calculate the LCM of 30225 and 30240.

LCM(30225,30240) = 3³ × 5² × 13¹ × 31¹ × 2⁵ × 7¹
LCM(30225,30240) = 60933600