What is the Least Common Multiple of 97200 and 97214?

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 97200 and 97214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 97200 and 97214, than apply into the LCM equation.

GCF(97200,97214) = 2
LCM(97200,97214) = ( 97200 × 97214) / 2
LCM(97200,97214) = 9449200800 / 2
LCM(97200,97214) = 4724600400

Least Common Multiple (LCM) of 97200 and 97214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 97200 and 97214. First we will calculate the prime factors of 97200 and 97214.

Prime Factorization of 97200

Prime Factorization of 97214

Now multiplying the highest exponent prime factors to calculate the LCM of 97200 and 97214.

LCM(97200,97214) = 2⁴ × 3⁵ × 5² × 13¹ × 3739¹
LCM(97200,97214) = 4724600400