What is the Least Common Multiple of 31400 and 31408?

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 31400 and 31408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31400 and 31408, than apply into the LCM equation.

GCF(31400,31408) = 8
LCM(31400,31408) = ( 31400 × 31408) / 8
LCM(31400,31408) = 986211200 / 8
LCM(31400,31408) = 123276400

Least Common Multiple (LCM) of 31400 and 31408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31400 and 31408. First we will calculate the prime factors of 31400 and 31408.

Prime Factorization of 31400

Prime Factorization of 31408

Now multiplying the highest exponent prime factors to calculate the LCM of 31400 and 31408.

LCM(31400,31408) = 2⁴ × 5² × 157¹ × 13¹ × 151¹
LCM(31400,31408) = 123276400