What is the Least Common Multiple of 2401 and 2414?

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 2401 and 2414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2401 and 2414, than apply into the LCM equation.

GCF(2401,2414) = 1
LCM(2401,2414) = ( 2401 × 2414) / 1
LCM(2401,2414) = 5796014 / 1
LCM(2401,2414) = 5796014

Least Common Multiple (LCM) of 2401 and 2414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2401 and 2414. First we will calculate the prime factors of 2401 and 2414.

Prime Factorization of 2401

Prime Factorization of 2414

Now multiplying the highest exponent prime factors to calculate the LCM of 2401 and 2414.

LCM(2401,2414) = 7⁴ × 2¹ × 17¹ × 71¹
LCM(2401,2414) = 5796014