What is the Least Common Multiple of 3678 and 3696?

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 3696 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 3696, than apply into the LCM equation.

GCF(3678,3696) = 6
LCM(3678,3696) = ( 3678 × 3696) / 6
LCM(3678,3696) = 13593888 / 6
LCM(3678,3696) = 2265648

Least Common Multiple (LCM) of 3678 and 3696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3678 and 3696. First we will calculate the prime factors of 3678 and 3696.

Prime Factorization of 3678

Prime Factorization of 3696

Now multiplying the highest exponent prime factors to calculate the LCM of 3678 and 3696.

LCM(3678,3696) = 2⁴ × 3¹ × 613¹ × 7¹ × 11¹
LCM(3678,3696) = 2265648