What is the Least Common Multiple of 10724 and 10742?

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 10724 and 10742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10724 and 10742, than apply into the LCM equation.

GCF(10724,10742) = 2
LCM(10724,10742) = ( 10724 × 10742) / 2
LCM(10724,10742) = 115197208 / 2
LCM(10724,10742) = 57598604

Least Common Multiple (LCM) of 10724 and 10742 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10724 and 10742. First we will calculate the prime factors of 10724 and 10742.

Prime Factorization of 10724

Prime Factorization of 10742

Now multiplying the highest exponent prime factors to calculate the LCM of 10724 and 10742.

LCM(10724,10742) = 2² × 7¹ × 383¹ × 41¹ × 131¹
LCM(10724,10742) = 57598604