What is the Least Common Multiple of 31000 and 31005?

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 31000 and 31005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31000 and 31005, than apply into the LCM equation.

GCF(31000,31005) = 5
LCM(31000,31005) = ( 31000 × 31005) / 5
LCM(31000,31005) = 961155000 / 5
LCM(31000,31005) = 192231000

Least Common Multiple (LCM) of 31000 and 31005 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31000 and 31005. First we will calculate the prime factors of 31000 and 31005.

Prime Factorization of 31000

Prime Factorization of 31005

Now multiplying the highest exponent prime factors to calculate the LCM of 31000 and 31005.

LCM(31000,31005) = 2³ × 5³ × 31¹ × 3² × 13¹ × 53¹
LCM(31000,31005) = 192231000