What is the Least Common Multiple of 8405 and 8414?

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 8405 and 8414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8405 and 8414, than apply into the LCM equation.

GCF(8405,8414) = 1
LCM(8405,8414) = ( 8405 × 8414) / 1
LCM(8405,8414) = 70719670 / 1
LCM(8405,8414) = 70719670

Least Common Multiple (LCM) of 8405 and 8414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8405 and 8414. First we will calculate the prime factors of 8405 and 8414.

Prime Factorization of 8405

Prime Factorization of 8414

Now multiplying the highest exponent prime factors to calculate the LCM of 8405 and 8414.

LCM(8405,8414) = 5¹ × 41² × 2¹ × 7¹ × 601¹
LCM(8405,8414) = 70719670