What is the Least Common Multiple of 42400 and 42405?

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 42400 and 42405 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42400 and 42405, than apply into the LCM equation.

GCF(42400,42405) = 5
LCM(42400,42405) = ( 42400 × 42405) / 5
LCM(42400,42405) = 1797972000 / 5
LCM(42400,42405) = 359594400

Least Common Multiple (LCM) of 42400 and 42405 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42400 and 42405. First we will calculate the prime factors of 42400 and 42405.

Prime Factorization of 42400

Prime Factorization of 42405

Now multiplying the highest exponent prime factors to calculate the LCM of 42400 and 42405.

LCM(42400,42405) = 2⁵ × 5² × 53¹ × 3¹ × 11¹ × 257¹
LCM(42400,42405) = 359594400