What is the Least Common Multiple of 12405 and 12420?

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 12405 and 12420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12405 and 12420, than apply into the LCM equation.

GCF(12405,12420) = 15
LCM(12405,12420) = ( 12405 × 12420) / 15
LCM(12405,12420) = 154070100 / 15
LCM(12405,12420) = 10271340

Least Common Multiple (LCM) of 12405 and 12420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12405 and 12420. First we will calculate the prime factors of 12405 and 12420.

Prime Factorization of 12405

Prime Factorization of 12420

Now multiplying the highest exponent prime factors to calculate the LCM of 12405 and 12420.

LCM(12405,12420) = 3³ × 5¹ × 827¹ × 2² × 23¹
LCM(12405,12420) = 10271340