What is the Least Common Multiple of 37208 and 37214?

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 37208 and 37214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37208 and 37214, than apply into the LCM equation.

GCF(37208,37214) = 2
LCM(37208,37214) = ( 37208 × 37214) / 2
LCM(37208,37214) = 1384658512 / 2
LCM(37208,37214) = 692329256

Least Common Multiple (LCM) of 37208 and 37214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37208 and 37214. First we will calculate the prime factors of 37208 and 37214.

Prime Factorization of 37208

Prime Factorization of 37214

Now multiplying the highest exponent prime factors to calculate the LCM of 37208 and 37214.

LCM(37208,37214) = 2³ × 4651¹ × 23¹ × 809¹
LCM(37208,37214) = 692329256