What is the Least Common Multiple of 39744 and 39762?

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 39744 and 39762 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39744 and 39762, than apply into the LCM equation.

GCF(39744,39762) = 18
LCM(39744,39762) = ( 39744 × 39762) / 18
LCM(39744,39762) = 1580300928 / 18
LCM(39744,39762) = 87794496

Least Common Multiple (LCM) of 39744 and 39762 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39744 and 39762. First we will calculate the prime factors of 39744 and 39762.

Prime Factorization of 39744

Prime Factorization of 39762

Now multiplying the highest exponent prime factors to calculate the LCM of 39744 and 39762.

LCM(39744,39762) = 2⁶ × 3³ × 23¹ × 47²
LCM(39744,39762) = 87794496