What is the Least Common Multiple of 3840 and 3854?

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 3840 and 3854 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3840 and 3854, than apply into the LCM equation.

GCF(3840,3854) = 2
LCM(3840,3854) = ( 3840 × 3854) / 2
LCM(3840,3854) = 14799360 / 2
LCM(3840,3854) = 7399680

Least Common Multiple (LCM) of 3840 and 3854 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3840 and 3854. First we will calculate the prime factors of 3840 and 3854.

Prime Factorization of 3840

Prime Factorization of 3854

Now multiplying the highest exponent prime factors to calculate the LCM of 3840 and 3854.

LCM(3840,3854) = 2⁸ × 3¹ × 5¹ × 41¹ × 47¹
LCM(3840,3854) = 7399680