What is the Least Common Multiple of 17400 and 17408?

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 17400 and 17408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17400 and 17408, than apply into the LCM equation.

GCF(17400,17408) = 8
LCM(17400,17408) = ( 17400 × 17408) / 8
LCM(17400,17408) = 302899200 / 8
LCM(17400,17408) = 37862400

Least Common Multiple (LCM) of 17400 and 17408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17400 and 17408. First we will calculate the prime factors of 17400 and 17408.

Prime Factorization of 17400

Prime Factorization of 17408

Now multiplying the highest exponent prime factors to calculate the LCM of 17400 and 17408.

LCM(17400,17408) = 2¹⁰ × 3¹ × 5² × 29¹ × 17¹
LCM(17400,17408) = 37862400