What is the Least Common Multiple of 32768 and 32772?

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 32772 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 32772, than apply into the LCM equation.

GCF(32768,32772) = 4
LCM(32768,32772) = ( 32768 × 32772) / 4
LCM(32768,32772) = 1073872896 / 4
LCM(32768,32772) = 268468224

Least Common Multiple (LCM) of 32768 and 32772 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32768 and 32772. First we will calculate the prime factors of 32768 and 32772.

Prime Factorization of 32768

Prime Factorization of 32772

Now multiplying the highest exponent prime factors to calculate the LCM of 32768 and 32772.

LCM(32768,32772) = 2¹⁵ × 3¹ × 2731¹
LCM(32768,32772) = 268468224