What is the Least Common Multiple of 17640 and 17657?

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 17640 and 17657 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17640 and 17657, than apply into the LCM equation.

GCF(17640,17657) = 1
LCM(17640,17657) = ( 17640 × 17657) / 1
LCM(17640,17657) = 311469480 / 1
LCM(17640,17657) = 311469480

Least Common Multiple (LCM) of 17640 and 17657 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17640 and 17657. First we will calculate the prime factors of 17640 and 17657.

Prime Factorization of 17640

Prime Factorization of 17657

Now multiplying the highest exponent prime factors to calculate the LCM of 17640 and 17657.

LCM(17640,17657) = 2³ × 3² × 5¹ × 7² × 17657¹
LCM(17640,17657) = 311469480