What is the Least Common Multiple of 57825 and 57840?

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 57825 and 57840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57825 and 57840, than apply into the LCM equation.

GCF(57825,57840) = 15
LCM(57825,57840) = ( 57825 × 57840) / 15
LCM(57825,57840) = 3344598000 / 15
LCM(57825,57840) = 222973200

Least Common Multiple (LCM) of 57825 and 57840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57825 and 57840. First we will calculate the prime factors of 57825 and 57840.

Prime Factorization of 57825

Prime Factorization of 57840

Now multiplying the highest exponent prime factors to calculate the LCM of 57825 and 57840.

LCM(57825,57840) = 3² × 5² × 257¹ × 2⁴ × 241¹
LCM(57825,57840) = 222973200