What is the Least Common Multiple of 31839 and 31854?

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 31839 and 31854 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31839 and 31854, than apply into the LCM equation.

GCF(31839,31854) = 3
LCM(31839,31854) = ( 31839 × 31854) / 3
LCM(31839,31854) = 1014199506 / 3
LCM(31839,31854) = 338066502

Least Common Multiple (LCM) of 31839 and 31854 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31839 and 31854. First we will calculate the prime factors of 31839 and 31854.

Prime Factorization of 31839

Prime Factorization of 31854

Now multiplying the highest exponent prime factors to calculate the LCM of 31839 and 31854.

LCM(31839,31854) = 3¹ × 10613¹ × 2¹ × 5309¹
LCM(31839,31854) = 338066502