What is the Least Common Multiple of 10170 and 10185?

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 10170 and 10185 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10170 and 10185, than apply into the LCM equation.

GCF(10170,10185) = 15
LCM(10170,10185) = ( 10170 × 10185) / 15
LCM(10170,10185) = 103581450 / 15
LCM(10170,10185) = 6905430

Least Common Multiple (LCM) of 10170 and 10185 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10170 and 10185. First we will calculate the prime factors of 10170 and 10185.

Prime Factorization of 10170

Prime Factorization of 10185

Now multiplying the highest exponent prime factors to calculate the LCM of 10170 and 10185.

LCM(10170,10185) = 2¹ × 3² × 5¹ × 113¹ × 7¹ × 97¹
LCM(10170,10185) = 6905430