What is the Least Common Multiple of 9200 and 9214?

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 9200 and 9214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9200 and 9214, than apply into the LCM equation.

GCF(9200,9214) = 2
LCM(9200,9214) = ( 9200 × 9214) / 2
LCM(9200,9214) = 84768800 / 2
LCM(9200,9214) = 42384400

Least Common Multiple (LCM) of 9200 and 9214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9200 and 9214. First we will calculate the prime factors of 9200 and 9214.

Prime Factorization of 9200

Prime Factorization of 9214

Now multiplying the highest exponent prime factors to calculate the LCM of 9200 and 9214.

LCM(9200,9214) = 2⁴ × 5² × 23¹ × 17¹ × 271¹
LCM(9200,9214) = 42384400