What is the Least Common Multiple of 3680 and 3699?

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 3680 and 3699 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3680 and 3699, than apply into the LCM equation.

GCF(3680,3699) = 1
LCM(3680,3699) = ( 3680 × 3699) / 1
LCM(3680,3699) = 13612320 / 1
LCM(3680,3699) = 13612320

Least Common Multiple (LCM) of 3680 and 3699 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3680 and 3699. First we will calculate the prime factors of 3680 and 3699.

Prime Factorization of 3680

Prime Factorization of 3699

Now multiplying the highest exponent prime factors to calculate the LCM of 3680 and 3699.

LCM(3680,3699) = 2⁵ × 5¹ × 23¹ × 3³ × 137¹
LCM(3680,3699) = 13612320