What is the Least Common Multiple of 42405 and 42420?

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 42405 and 42420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42405 and 42420, than apply into the LCM equation.

GCF(42405,42420) = 15
LCM(42405,42420) = ( 42405 × 42420) / 15
LCM(42405,42420) = 1798820100 / 15
LCM(42405,42420) = 119921340

Least Common Multiple (LCM) of 42405 and 42420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42405 and 42420. First we will calculate the prime factors of 42405 and 42420.

Prime Factorization of 42405

Prime Factorization of 42420

Now multiplying the highest exponent prime factors to calculate the LCM of 42405 and 42420.

LCM(42405,42420) = 3¹ × 5¹ × 11¹ × 257¹ × 2² × 7¹ × 101¹
LCM(42405,42420) = 119921340