What is the Least Common Multiple of 82208 and 82216?

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 82208 and 82216 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82208 and 82216, than apply into the LCM equation.

GCF(82208,82216) = 8
LCM(82208,82216) = ( 82208 × 82216) / 8
LCM(82208,82216) = 6758812928 / 8
LCM(82208,82216) = 844851616

Least Common Multiple (LCM) of 82208 and 82216 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82208 and 82216. First we will calculate the prime factors of 82208 and 82216.

Prime Factorization of 82208

Prime Factorization of 82216

Now multiplying the highest exponent prime factors to calculate the LCM of 82208 and 82216.

LCM(82208,82216) = 2⁵ × 7¹ × 367¹ × 43¹ × 239¹
LCM(82208,82216) = 844851616