What is the Least Common Multiple of 32768 and 32782?

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 32768 and 32782 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32768 and 32782, than apply into the LCM equation.

GCF(32768,32782) = 2
LCM(32768,32782) = ( 32768 × 32782) / 2
LCM(32768,32782) = 1074200576 / 2
LCM(32768,32782) = 537100288

Least Common Multiple (LCM) of 32768 and 32782 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32768 and 32782. First we will calculate the prime factors of 32768 and 32782.

Prime Factorization of 32768

Prime Factorization of 32782

Now multiplying the highest exponent prime factors to calculate the LCM of 32768 and 32782.

LCM(32768,32782) = 2¹⁵ × 37¹ × 443¹
LCM(32768,32782) = 537100288