What is the Least Common Multiple of 17700 and 17712?

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 17700 and 17712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17700 and 17712, than apply into the LCM equation.

GCF(17700,17712) = 12
LCM(17700,17712) = ( 17700 × 17712) / 12
LCM(17700,17712) = 313502400 / 12
LCM(17700,17712) = 26125200

Least Common Multiple (LCM) of 17700 and 17712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17700 and 17712. First we will calculate the prime factors of 17700 and 17712.

Prime Factorization of 17700

Prime Factorization of 17712

Now multiplying the highest exponent prime factors to calculate the LCM of 17700 and 17712.

LCM(17700,17712) = 2⁴ × 3³ × 5² × 59¹ × 41¹
LCM(17700,17712) = 26125200