What is the Least Common Multiple of 3678 and 3697?

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 3678 and 3697 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3678 and 3697, than apply into the LCM equation.

GCF(3678,3697) = 1
LCM(3678,3697) = ( 3678 × 3697) / 1
LCM(3678,3697) = 13597566 / 1
LCM(3678,3697) = 13597566

Least Common Multiple (LCM) of 3678 and 3697 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3678 and 3697. First we will calculate the prime factors of 3678 and 3697.

Prime Factorization of 3678

Prime Factorization of 3697

Now multiplying the highest exponent prime factors to calculate the LCM of 3678 and 3697.

LCM(3678,3697) = 2¹ × 3¹ × 613¹ × 3697¹
LCM(3678,3697) = 13597566