What is the Least Common Multiple of 71200 and 71214?

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 71200 and 71214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71200 and 71214, than apply into the LCM equation.

GCF(71200,71214) = 2
LCM(71200,71214) = ( 71200 × 71214) / 2
LCM(71200,71214) = 5070436800 / 2
LCM(71200,71214) = 2535218400

Least Common Multiple (LCM) of 71200 and 71214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71200 and 71214. First we will calculate the prime factors of 71200 and 71214.

Prime Factorization of 71200

Prime Factorization of 71214

Now multiplying the highest exponent prime factors to calculate the LCM of 71200 and 71214.

LCM(71200,71214) = 2⁵ × 5² × 89¹ × 3¹ × 11¹ × 13¹ × 83¹
LCM(71200,71214) = 2535218400