What is the Least Common Multiple of 82170 and 82188?

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 82170 and 82188 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82170 and 82188, than apply into the LCM equation.

GCF(82170,82188) = 18
LCM(82170,82188) = ( 82170 × 82188) / 18
LCM(82170,82188) = 6753387960 / 18
LCM(82170,82188) = 375188220

Least Common Multiple (LCM) of 82170 and 82188 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82170 and 82188. First we will calculate the prime factors of 82170 and 82188.

Prime Factorization of 82170

Prime Factorization of 82188

Now multiplying the highest exponent prime factors to calculate the LCM of 82170 and 82188.

LCM(82170,82188) = 2² × 3³ × 5¹ × 11¹ × 83¹ × 761¹
LCM(82170,82188) = 375188220