What is the Least Common Multiple of 3696 and 3705?

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 3696 and 3705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3696 and 3705, than apply into the LCM equation.

GCF(3696,3705) = 3
LCM(3696,3705) = ( 3696 × 3705) / 3
LCM(3696,3705) = 13693680 / 3
LCM(3696,3705) = 4564560

Least Common Multiple (LCM) of 3696 and 3705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3696 and 3705. First we will calculate the prime factors of 3696 and 3705.

Prime Factorization of 3696

Prime Factorization of 3705

Now multiplying the highest exponent prime factors to calculate the LCM of 3696 and 3705.

LCM(3696,3705) = 2⁴ × 3¹ × 7¹ × 11¹ × 5¹ × 13¹ × 19¹
LCM(3696,3705) = 4564560