What is the Least Common Multiple of 78192 and 78208?

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 78192 and 78208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78192 and 78208, than apply into the LCM equation.

GCF(78192,78208) = 16
LCM(78192,78208) = ( 78192 × 78208) / 16
LCM(78192,78208) = 6115239936 / 16
LCM(78192,78208) = 382202496

Least Common Multiple (LCM) of 78192 and 78208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78192 and 78208. First we will calculate the prime factors of 78192 and 78208.

Prime Factorization of 78192

Prime Factorization of 78208

Now multiplying the highest exponent prime factors to calculate the LCM of 78192 and 78208.

LCM(78192,78208) = 2⁷ × 3³ × 181¹ × 13¹ × 47¹
LCM(78192,78208) = 382202496