What is the Least Common Multiple of 8080 and 8084?

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 8080 and 8084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8080 and 8084, than apply into the LCM equation.

GCF(8080,8084) = 4
LCM(8080,8084) = ( 8080 × 8084) / 4
LCM(8080,8084) = 65318720 / 4
LCM(8080,8084) = 16329680

Least Common Multiple (LCM) of 8080 and 8084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8080 and 8084. First we will calculate the prime factors of 8080 and 8084.

Prime Factorization of 8080

Prime Factorization of 8084

Now multiplying the highest exponent prime factors to calculate the LCM of 8080 and 8084.

LCM(8080,8084) = 2⁴ × 5¹ × 101¹ × 43¹ × 47¹
LCM(8080,8084) = 16329680