What is the Least Common Multiple of 83744 and 83760?

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 83744 and 83760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 83744 and 83760, than apply into the LCM equation.

GCF(83744,83760) = 16
LCM(83744,83760) = ( 83744 × 83760) / 16
LCM(83744,83760) = 7014397440 / 16
LCM(83744,83760) = 438399840

Least Common Multiple (LCM) of 83744 and 83760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 83744 and 83760. First we will calculate the prime factors of 83744 and 83760.

Prime Factorization of 83744

Prime Factorization of 83760

Now multiplying the highest exponent prime factors to calculate the LCM of 83744 and 83760.

LCM(83744,83760) = 2⁵ × 2617¹ × 3¹ × 5¹ × 349¹
LCM(83744,83760) = 438399840