What is the Least Common Multiple of 8400 and 8409?

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 8400 and 8409 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8400 and 8409, than apply into the LCM equation.

GCF(8400,8409) = 3
LCM(8400,8409) = ( 8400 × 8409) / 3
LCM(8400,8409) = 70635600 / 3
LCM(8400,8409) = 23545200

Least Common Multiple (LCM) of 8400 and 8409 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8400 and 8409. First we will calculate the prime factors of 8400 and 8409.

Prime Factorization of 8400

Prime Factorization of 8409

Now multiplying the highest exponent prime factors to calculate the LCM of 8400 and 8409.

LCM(8400,8409) = 2⁴ × 3¹ × 5² × 7¹ × 2803¹
LCM(8400,8409) = 23545200