What is the Least Common Multiple of 8400 and 8404?

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 8404 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 8404, than apply into the LCM equation.

GCF(8400,8404) = 4
LCM(8400,8404) = ( 8400 × 8404) / 4
LCM(8400,8404) = 70593600 / 4
LCM(8400,8404) = 17648400

Least Common Multiple (LCM) of 8400 and 8404 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8400 and 8404. First we will calculate the prime factors of 8400 and 8404.

Prime Factorization of 8400

Prime Factorization of 8404

Now multiplying the highest exponent prime factors to calculate the LCM of 8400 and 8404.

LCM(8400,8404) = 2⁴ × 3¹ × 5² × 7¹ × 11¹ × 191¹
LCM(8400,8404) = 17648400