What is the Least Common Multiple of 5728 and 5748?

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 5728 and 5748 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5728 and 5748, than apply into the LCM equation.

GCF(5728,5748) = 4
LCM(5728,5748) = ( 5728 × 5748) / 4
LCM(5728,5748) = 32924544 / 4
LCM(5728,5748) = 8231136

Least Common Multiple (LCM) of 5728 and 5748 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5728 and 5748. First we will calculate the prime factors of 5728 and 5748.

Prime Factorization of 5728

Prime Factorization of 5748

Now multiplying the highest exponent prime factors to calculate the LCM of 5728 and 5748.

LCM(5728,5748) = 2⁵ × 179¹ × 3¹ × 479¹
LCM(5728,5748) = 8231136