What is the Least Common Multiple of 30996 and 31000?

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 30996 and 31000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30996 and 31000, than apply into the LCM equation.

GCF(30996,31000) = 4
LCM(30996,31000) = ( 30996 × 31000) / 4
LCM(30996,31000) = 960876000 / 4
LCM(30996,31000) = 240219000

Least Common Multiple (LCM) of 30996 and 31000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30996 and 31000. First we will calculate the prime factors of 30996 and 31000.

Prime Factorization of 30996

Prime Factorization of 31000

Now multiplying the highest exponent prime factors to calculate the LCM of 30996 and 31000.

LCM(30996,31000) = 2³ × 3³ × 7¹ × 41¹ × 5³ × 31¹
LCM(30996,31000) = 240219000