What is the Least Common Multiple of 19995 and 20000?

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 19995 and 20000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19995 and 20000, than apply into the LCM equation.

GCF(19995,20000) = 5
LCM(19995,20000) = ( 19995 × 20000) / 5
LCM(19995,20000) = 399900000 / 5
LCM(19995,20000) = 79980000

Least Common Multiple (LCM) of 19995 and 20000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19995 and 20000. First we will calculate the prime factors of 19995 and 20000.

Prime Factorization of 19995

Prime Factorization of 20000

Now multiplying the highest exponent prime factors to calculate the LCM of 19995 and 20000.

LCM(19995,20000) = 3¹ × 5⁴ × 31¹ × 43¹ × 2⁵
LCM(19995,20000) = 79980000