What is the Least Common Multiple of 25200 and 25205?

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 25200 and 25205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25200 and 25205, than apply into the LCM equation.

GCF(25200,25205) = 5
LCM(25200,25205) = ( 25200 × 25205) / 5
LCM(25200,25205) = 635166000 / 5
LCM(25200,25205) = 127033200

Least Common Multiple (LCM) of 25200 and 25205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25200 and 25205. First we will calculate the prime factors of 25200 and 25205.

Prime Factorization of 25200

Prime Factorization of 25205

Now multiplying the highest exponent prime factors to calculate the LCM of 25200 and 25205.

LCM(25200,25205) = 2⁴ × 3² × 5² × 7¹ × 71²
LCM(25200,25205) = 127033200