What is the Least Common Multiple of 78208 and 78228?

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 78208 and 78228 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78208 and 78228, than apply into the LCM equation.

GCF(78208,78228) = 4
LCM(78208,78228) = ( 78208 × 78228) / 4
LCM(78208,78228) = 6118055424 / 4
LCM(78208,78228) = 1529513856

Least Common Multiple (LCM) of 78208 and 78228 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78208 and 78228. First we will calculate the prime factors of 78208 and 78228.

Prime Factorization of 78208

Prime Factorization of 78228

Now multiplying the highest exponent prime factors to calculate the LCM of 78208 and 78228.

LCM(78208,78228) = 2⁷ × 13¹ × 47¹ × 3² × 41¹ × 53¹
LCM(78208,78228) = 1529513856