What is the Least Common Multiple of 74200 and 74214?

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 74200 and 74214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 74200 and 74214, than apply into the LCM equation.

GCF(74200,74214) = 14
LCM(74200,74214) = ( 74200 × 74214) / 14
LCM(74200,74214) = 5506678800 / 14
LCM(74200,74214) = 393334200

Least Common Multiple (LCM) of 74200 and 74214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 74200 and 74214. First we will calculate the prime factors of 74200 and 74214.

Prime Factorization of 74200

Prime Factorization of 74214

Now multiplying the highest exponent prime factors to calculate the LCM of 74200 and 74214.

LCM(74200,74214) = 2³ × 5² × 7¹ × 53¹ × 3² × 19¹ × 31¹
LCM(74200,74214) = 393334200