What is the Least Common Multiple of 7408 and 7414?

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 7408 and 7414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7408 and 7414, than apply into the LCM equation.

GCF(7408,7414) = 2
LCM(7408,7414) = ( 7408 × 7414) / 2
LCM(7408,7414) = 54922912 / 2
LCM(7408,7414) = 27461456

Least Common Multiple (LCM) of 7408 and 7414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7408 and 7414. First we will calculate the prime factors of 7408 and 7414.

Prime Factorization of 7408

Prime Factorization of 7414

Now multiplying the highest exponent prime factors to calculate the LCM of 7408 and 7414.

LCM(7408,7414) = 2⁴ × 463¹ × 11¹ × 337¹
LCM(7408,7414) = 27461456