What is the Least Common Multiple of 31854 and 31874?

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 31854 and 31874 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31854 and 31874, than apply into the LCM equation.

GCF(31854,31874) = 2
LCM(31854,31874) = ( 31854 × 31874) / 2
LCM(31854,31874) = 1015314396 / 2
LCM(31854,31874) = 507657198

Least Common Multiple (LCM) of 31854 and 31874 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31854 and 31874. First we will calculate the prime factors of 31854 and 31874.

Prime Factorization of 31854

Prime Factorization of 31874

Now multiplying the highest exponent prime factors to calculate the LCM of 31854 and 31874.

LCM(31854,31874) = 2¹ × 3¹ × 5309¹ × 15937¹
LCM(31854,31874) = 507657198