What is the Least Common Multiple of 10749 and 10764?

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 10749 and 10764 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10749 and 10764, than apply into the LCM equation.

GCF(10749,10764) = 3
LCM(10749,10764) = ( 10749 × 10764) / 3
LCM(10749,10764) = 115702236 / 3
LCM(10749,10764) = 38567412

Least Common Multiple (LCM) of 10749 and 10764 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10749 and 10764. First we will calculate the prime factors of 10749 and 10764.

Prime Factorization of 10749

Prime Factorization of 10764

Now multiplying the highest exponent prime factors to calculate the LCM of 10749 and 10764.

LCM(10749,10764) = 3² × 3583¹ × 2² × 13¹ × 23¹
LCM(10749,10764) = 38567412