What is the Least Common Multiple of 17724 and 17742?

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 17724 and 17742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17724 and 17742, than apply into the LCM equation.

GCF(17724,17742) = 6
LCM(17724,17742) = ( 17724 × 17742) / 6
LCM(17724,17742) = 314459208 / 6
LCM(17724,17742) = 52409868

Least Common Multiple (LCM) of 17724 and 17742 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17724 and 17742. First we will calculate the prime factors of 17724 and 17742.

Prime Factorization of 17724

Prime Factorization of 17742

Now multiplying the highest exponent prime factors to calculate the LCM of 17724 and 17742.

LCM(17724,17742) = 2² × 3¹ × 7¹ × 211¹ × 2957¹
LCM(17724,17742) = 52409868