What is the Least Common Multiple of 8400 and 8418?

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 8418 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 8418, than apply into the LCM equation.

GCF(8400,8418) = 6
LCM(8400,8418) = ( 8400 × 8418) / 6
LCM(8400,8418) = 70711200 / 6
LCM(8400,8418) = 11785200

Least Common Multiple (LCM) of 8400 and 8418 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8400 and 8418. First we will calculate the prime factors of 8400 and 8418.

Prime Factorization of 8400

Prime Factorization of 8418

Now multiplying the highest exponent prime factors to calculate the LCM of 8400 and 8418.

LCM(8400,8418) = 2⁴ × 3¹ × 5² × 7¹ × 23¹ × 61¹
LCM(8400,8418) = 11785200