What is the Least Common Multiple of 10408 and 10414?

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 10408 and 10414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10408 and 10414, than apply into the LCM equation.

GCF(10408,10414) = 2
LCM(10408,10414) = ( 10408 × 10414) / 2
LCM(10408,10414) = 108388912 / 2
LCM(10408,10414) = 54194456

Least Common Multiple (LCM) of 10408 and 10414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10408 and 10414. First we will calculate the prime factors of 10408 and 10414.

Prime Factorization of 10408

Prime Factorization of 10414

Now multiplying the highest exponent prime factors to calculate the LCM of 10408 and 10414.

LCM(10408,10414) = 2³ × 1301¹ × 41¹ × 127¹
LCM(10408,10414) = 54194456