What is the Least Common Multiple of 31749 and 31764?

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 31749 and 31764 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31749 and 31764, than apply into the LCM equation.

GCF(31749,31764) = 3
LCM(31749,31764) = ( 31749 × 31764) / 3
LCM(31749,31764) = 1008475236 / 3
LCM(31749,31764) = 336158412

Least Common Multiple (LCM) of 31749 and 31764 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31749 and 31764. First we will calculate the prime factors of 31749 and 31764.

Prime Factorization of 31749

Prime Factorization of 31764

Now multiplying the highest exponent prime factors to calculate the LCM of 31749 and 31764.

LCM(31749,31764) = 3¹ × 19¹ × 557¹ × 2² × 2647¹
LCM(31749,31764) = 336158412