What is the Least Common Multiple of 37310 and 37314?

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 37310 and 37314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37310 and 37314, than apply into the LCM equation.

GCF(37310,37314) = 2
LCM(37310,37314) = ( 37310 × 37314) / 2
LCM(37310,37314) = 1392185340 / 2
LCM(37310,37314) = 696092670

Least Common Multiple (LCM) of 37310 and 37314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37310 and 37314. First we will calculate the prime factors of 37310 and 37314.

Prime Factorization of 37310

Prime Factorization of 37314

Now multiplying the highest exponent prime factors to calculate the LCM of 37310 and 37314.

LCM(37310,37314) = 2¹ × 5¹ × 7¹ × 13¹ × 41¹ × 3³ × 691¹
LCM(37310,37314) = 696092670