What is the Least Common Multiple of 31854 and 31870?

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 31870 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 31870, than apply into the LCM equation.

GCF(31854,31870) = 2
LCM(31854,31870) = ( 31854 × 31870) / 2
LCM(31854,31870) = 1015186980 / 2
LCM(31854,31870) = 507593490

Least Common Multiple (LCM) of 31854 and 31870 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31854 and 31870. First we will calculate the prime factors of 31854 and 31870.

Prime Factorization of 31854

Prime Factorization of 31870

Now multiplying the highest exponent prime factors to calculate the LCM of 31854 and 31870.

LCM(31854,31870) = 2¹ × 3¹ × 5309¹ × 5¹ × 3187¹
LCM(31854,31870) = 507593490