What is the Least Common Multiple of 24300 and 24314?

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 24300 and 24314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 24300 and 24314, than apply into the LCM equation.

GCF(24300,24314) = 2
LCM(24300,24314) = ( 24300 × 24314) / 2
LCM(24300,24314) = 590830200 / 2
LCM(24300,24314) = 295415100

Least Common Multiple (LCM) of 24300 and 24314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 24300 and 24314. First we will calculate the prime factors of 24300 and 24314.

Prime Factorization of 24300

Prime Factorization of 24314

Now multiplying the highest exponent prime factors to calculate the LCM of 24300 and 24314.

LCM(24300,24314) = 2² × 3⁵ × 5² × 12157¹
LCM(24300,24314) = 295415100