What is the Least Common Multiple of 39225 and 39240?

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 39225 and 39240 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39225 and 39240, than apply into the LCM equation.

GCF(39225,39240) = 15
LCM(39225,39240) = ( 39225 × 39240) / 15
LCM(39225,39240) = 1539189000 / 15
LCM(39225,39240) = 102612600

Least Common Multiple (LCM) of 39225 and 39240 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39225 and 39240. First we will calculate the prime factors of 39225 and 39240.

Prime Factorization of 39225

Prime Factorization of 39240

Now multiplying the highest exponent prime factors to calculate the LCM of 39225 and 39240.

LCM(39225,39240) = 3² × 5² × 523¹ × 2³ × 109¹
LCM(39225,39240) = 102612600