What is the Least Common Multiple of 8084 and 8100?

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 8084 and 8100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8084 and 8100, than apply into the LCM equation.

GCF(8084,8100) = 4
LCM(8084,8100) = ( 8084 × 8100) / 4
LCM(8084,8100) = 65480400 / 4
LCM(8084,8100) = 16370100

Least Common Multiple (LCM) of 8084 and 8100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8084 and 8100. First we will calculate the prime factors of 8084 and 8100.

Prime Factorization of 8084

Prime Factorization of 8100

Now multiplying the highest exponent prime factors to calculate the LCM of 8084 and 8100.

LCM(8084,8100) = 2² × 43¹ × 47¹ × 3⁴ × 5²
LCM(8084,8100) = 16370100