What is the Least Common Multiple of 20408 and 20414?

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 20408 and 20414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20408 and 20414, than apply into the LCM equation.

GCF(20408,20414) = 2
LCM(20408,20414) = ( 20408 × 20414) / 2
LCM(20408,20414) = 416608912 / 2
LCM(20408,20414) = 208304456

Least Common Multiple (LCM) of 20408 and 20414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20408 and 20414. First we will calculate the prime factors of 20408 and 20414.

Prime Factorization of 20408

Prime Factorization of 20414

Now multiplying the highest exponent prime factors to calculate the LCM of 20408 and 20414.

LCM(20408,20414) = 2³ × 2551¹ × 59¹ × 173¹
LCM(20408,20414) = 208304456