What is the Least Common Multiple of 3654 and 3670?

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 3654 and 3670 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3654 and 3670, than apply into the LCM equation.

GCF(3654,3670) = 2
LCM(3654,3670) = ( 3654 × 3670) / 2
LCM(3654,3670) = 13410180 / 2
LCM(3654,3670) = 6705090

Least Common Multiple (LCM) of 3654 and 3670 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3654 and 3670. First we will calculate the prime factors of 3654 and 3670.

Prime Factorization of 3654

Prime Factorization of 3670

Now multiplying the highest exponent prime factors to calculate the LCM of 3654 and 3670.

LCM(3654,3670) = 2¹ × 3² × 7¹ × 29¹ × 5¹ × 367¹
LCM(3654,3670) = 6705090