What is the Least Common Multiple of 19744 and 19752?

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 19744 and 19752 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19744 and 19752, than apply into the LCM equation.

GCF(19744,19752) = 8
LCM(19744,19752) = ( 19744 × 19752) / 8
LCM(19744,19752) = 389983488 / 8
LCM(19744,19752) = 48747936

Least Common Multiple (LCM) of 19744 and 19752 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19744 and 19752. First we will calculate the prime factors of 19744 and 19752.

Prime Factorization of 19744

Prime Factorization of 19752

Now multiplying the highest exponent prime factors to calculate the LCM of 19744 and 19752.

LCM(19744,19752) = 2⁵ × 617¹ × 3¹ × 823¹
LCM(19744,19752) = 48747936