What is the Least Common Multiple of 16400 and 16405?

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 16400 and 16405 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16400 and 16405, than apply into the LCM equation.

GCF(16400,16405) = 5
LCM(16400,16405) = ( 16400 × 16405) / 5
LCM(16400,16405) = 269042000 / 5
LCM(16400,16405) = 53808400

Least Common Multiple (LCM) of 16400 and 16405 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16400 and 16405. First we will calculate the prime factors of 16400 and 16405.

Prime Factorization of 16400

Prime Factorization of 16405

Now multiplying the highest exponent prime factors to calculate the LCM of 16400 and 16405.

LCM(16400,16405) = 2⁴ × 5² × 41¹ × 17¹ × 193¹
LCM(16400,16405) = 53808400