What is the Least Common Multiple of 38400 and 38409?

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 38400 and 38409 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38400 and 38409, than apply into the LCM equation.

GCF(38400,38409) = 3
LCM(38400,38409) = ( 38400 × 38409) / 3
LCM(38400,38409) = 1474905600 / 3
LCM(38400,38409) = 491635200

Least Common Multiple (LCM) of 38400 and 38409 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38400 and 38409. First we will calculate the prime factors of 38400 and 38409.

Prime Factorization of 38400

Prime Factorization of 38409

Now multiplying the highest exponent prime factors to calculate the LCM of 38400 and 38409.

LCM(38400,38409) = 2⁹ × 3¹ × 5² × 7¹ × 31¹ × 59¹
LCM(38400,38409) = 491635200