What is the Least Common Multiple of 5709 and 5728?

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 5728 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 5728, than apply into the LCM equation.

GCF(5709,5728) = 1
LCM(5709,5728) = ( 5709 × 5728) / 1
LCM(5709,5728) = 32701152 / 1
LCM(5709,5728) = 32701152

Least Common Multiple (LCM) of 5709 and 5728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5709 and 5728. First we will calculate the prime factors of 5709 and 5728.

Prime Factorization of 5709

Prime Factorization of 5728

Now multiplying the highest exponent prime factors to calculate the LCM of 5709 and 5728.

LCM(5709,5728) = 3¹ × 11¹ × 173¹ × 2⁵ × 179¹
LCM(5709,5728) = 32701152