What is the Least Common Multiple of 40000 and 40012?

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 40000 and 40012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40000 and 40012, than apply into the LCM equation.

GCF(40000,40012) = 4
LCM(40000,40012) = ( 40000 × 40012) / 4
LCM(40000,40012) = 1600480000 / 4
LCM(40000,40012) = 400120000

Least Common Multiple (LCM) of 40000 and 40012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40000 and 40012. First we will calculate the prime factors of 40000 and 40012.

Prime Factorization of 40000

Prime Factorization of 40012

Now multiplying the highest exponent prime factors to calculate the LCM of 40000 and 40012.

LCM(40000,40012) = 2⁶ × 5⁴ × 7¹ × 1429¹
LCM(40000,40012) = 400120000