What is the Least Common Multiple of 51600 and 51612?

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 51600 and 51612 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51600 and 51612, than apply into the LCM equation.

GCF(51600,51612) = 12
LCM(51600,51612) = ( 51600 × 51612) / 12
LCM(51600,51612) = 2663179200 / 12
LCM(51600,51612) = 221931600

Least Common Multiple (LCM) of 51600 and 51612 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51600 and 51612. First we will calculate the prime factors of 51600 and 51612.

Prime Factorization of 51600

Prime Factorization of 51612

Now multiplying the highest exponent prime factors to calculate the LCM of 51600 and 51612.

LCM(51600,51612) = 2⁴ × 3¹ × 5² × 43¹ × 11¹ × 17¹ × 23¹
LCM(51600,51612) = 221931600