What is the Least Common Multiple of 5709 and 5724?

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 5709 and 5724 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5709 and 5724, than apply into the LCM equation.

GCF(5709,5724) = 3
LCM(5709,5724) = ( 5709 × 5724) / 3
LCM(5709,5724) = 32678316 / 3
LCM(5709,5724) = 10892772

Least Common Multiple (LCM) of 5709 and 5724 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5709 and 5724. First we will calculate the prime factors of 5709 and 5724.

Prime Factorization of 5709

Prime Factorization of 5724

Now multiplying the highest exponent prime factors to calculate the LCM of 5709 and 5724.

LCM(5709,5724) = 3³ × 11¹ × 173¹ × 2² × 53¹
LCM(5709,5724) = 10892772