What is the Least Common Multiple of 40080 and 40100?

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 40080 and 40100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40080 and 40100, than apply into the LCM equation.

GCF(40080,40100) = 20
LCM(40080,40100) = ( 40080 × 40100) / 20
LCM(40080,40100) = 1607208000 / 20
LCM(40080,40100) = 80360400

Least Common Multiple (LCM) of 40080 and 40100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40080 and 40100. First we will calculate the prime factors of 40080 and 40100.

Prime Factorization of 40080

Prime Factorization of 40100

Now multiplying the highest exponent prime factors to calculate the LCM of 40080 and 40100.

LCM(40080,40100) = 2⁴ × 3¹ × 5² × 167¹ × 401¹
LCM(40080,40100) = 80360400