What is the Least Common Multiple of 32748 and 32768?

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 32748 and 32768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32748 and 32768, than apply into the LCM equation.

GCF(32748,32768) = 4
LCM(32748,32768) = ( 32748 × 32768) / 4
LCM(32748,32768) = 1073086464 / 4
LCM(32748,32768) = 268271616

Least Common Multiple (LCM) of 32748 and 32768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32748 and 32768. First we will calculate the prime factors of 32748 and 32768.

Prime Factorization of 32748

Prime Factorization of 32768

Now multiplying the highest exponent prime factors to calculate the LCM of 32748 and 32768.

LCM(32748,32768) = 2¹⁵ × 3¹ × 2729¹
LCM(32748,32768) = 268271616