What is the Least Common Multiple of 41200 and 41214?

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 41200 and 41214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 41200 and 41214, than apply into the LCM equation.

GCF(41200,41214) = 2
LCM(41200,41214) = ( 41200 × 41214) / 2
LCM(41200,41214) = 1698016800 / 2
LCM(41200,41214) = 849008400

Least Common Multiple (LCM) of 41200 and 41214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 41200 and 41214. First we will calculate the prime factors of 41200 and 41214.

Prime Factorization of 41200

Prime Factorization of 41214

Now multiplying the highest exponent prime factors to calculate the LCM of 41200 and 41214.

LCM(41200,41214) = 2⁴ × 5² × 103¹ × 3¹ × 6869¹
LCM(41200,41214) = 849008400