What is the Least Common Multiple of 51585 and 51600?

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 51585 and 51600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51585 and 51600, than apply into the LCM equation.

GCF(51585,51600) = 15
LCM(51585,51600) = ( 51585 × 51600) / 15
LCM(51585,51600) = 2661786000 / 15
LCM(51585,51600) = 177452400

Least Common Multiple (LCM) of 51585 and 51600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51585 and 51600. First we will calculate the prime factors of 51585 and 51600.

Prime Factorization of 51585

Prime Factorization of 51600

Now multiplying the highest exponent prime factors to calculate the LCM of 51585 and 51600.

LCM(51585,51600) = 3¹ × 5² × 19¹ × 181¹ × 2⁴ × 43¹
LCM(51585,51600) = 177452400