What is the Least Common Multiple of 57225 and 57240?

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 57225 and 57240 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57225 and 57240, than apply into the LCM equation.

GCF(57225,57240) = 15
LCM(57225,57240) = ( 57225 × 57240) / 15
LCM(57225,57240) = 3275559000 / 15
LCM(57225,57240) = 218370600

Least Common Multiple (LCM) of 57225 and 57240 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57225 and 57240. First we will calculate the prime factors of 57225 and 57240.

Prime Factorization of 57225

Prime Factorization of 57240

Now multiplying the highest exponent prime factors to calculate the LCM of 57225 and 57240.

LCM(57225,57240) = 3³ × 5² × 7¹ × 109¹ × 2³ × 53¹
LCM(57225,57240) = 218370600