What is the Least Common Multiple of 39744 and 39760?

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 39760 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 39760, than apply into the LCM equation.

GCF(39744,39760) = 16
LCM(39744,39760) = ( 39744 × 39760) / 16
LCM(39744,39760) = 1580221440 / 16
LCM(39744,39760) = 98763840

Least Common Multiple (LCM) of 39744 and 39760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39744 and 39760. First we will calculate the prime factors of 39744 and 39760.

Prime Factorization of 39744

Prime Factorization of 39760

Now multiplying the highest exponent prime factors to calculate the LCM of 39744 and 39760.

LCM(39744,39760) = 2⁶ × 3³ × 23¹ × 5¹ × 7¹ × 71¹
LCM(39744,39760) = 98763840