What is the Least Common Multiple of 17744 and 17748?

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 17744 and 17748 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17744 and 17748, than apply into the LCM equation.

GCF(17744,17748) = 4
LCM(17744,17748) = ( 17744 × 17748) / 4
LCM(17744,17748) = 314920512 / 4
LCM(17744,17748) = 78730128

Least Common Multiple (LCM) of 17744 and 17748 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17744 and 17748. First we will calculate the prime factors of 17744 and 17748.

Prime Factorization of 17744

Prime Factorization of 17748

Now multiplying the highest exponent prime factors to calculate the LCM of 17744 and 17748.

LCM(17744,17748) = 2⁴ × 1109¹ × 3² × 17¹ × 29¹
LCM(17744,17748) = 78730128