What is the Least Common Multiple of 3688 and 3700?

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 3688 and 3700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3688 and 3700, than apply into the LCM equation.

GCF(3688,3700) = 4
LCM(3688,3700) = ( 3688 × 3700) / 4
LCM(3688,3700) = 13645600 / 4
LCM(3688,3700) = 3411400

Least Common Multiple (LCM) of 3688 and 3700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3688 and 3700. First we will calculate the prime factors of 3688 and 3700.

Prime Factorization of 3688

Prime Factorization of 3700

Now multiplying the highest exponent prime factors to calculate the LCM of 3688 and 3700.

LCM(3688,3700) = 2³ × 461¹ × 5² × 37¹
LCM(3688,3700) = 3411400