What is the Least Common Multiple of 69186 and 69200?

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 69186 and 69200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69186 and 69200, than apply into the LCM equation.

GCF(69186,69200) = 2
LCM(69186,69200) = ( 69186 × 69200) / 2
LCM(69186,69200) = 4787671200 / 2
LCM(69186,69200) = 2393835600

Least Common Multiple (LCM) of 69186 and 69200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69186 and 69200. First we will calculate the prime factors of 69186 and 69200.

Prime Factorization of 69186

Prime Factorization of 69200

Now multiplying the highest exponent prime factors to calculate the LCM of 69186 and 69200.

LCM(69186,69200) = 2⁴ × 3¹ × 13¹ × 887¹ × 5² × 173¹
LCM(69186,69200) = 2393835600