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What is the Least Common Multiple of 16172 and 16185?

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 (LCM) of 16172 and 16185 is 20134140.

LCM(16172,16185) = 20134140

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Least Common Multiple of 16172 and 16185 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16172 and 16185, than apply into the LCM equation.

GCF(16172,16185) = 13
LCM(16172,16185) = ( 16172 × 16185) / 13
LCM(16172,16185) = 261743820 / 13
LCM(16172,16185) = 20134140

Least Common Multiple (LCM) of 16172 and 16185 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16172 and 16185. First we will calculate the prime factors of 16172 and 16185.

Prime Factorization of 16172

Prime factors of 16172 are 2, 13, 311. Prime factorization of 16172 in exponential form is:

16172 = 22 × 131 × 3111

Prime Factorization of 16185

Prime factors of 16185 are 3, 5, 13, 83. Prime factorization of 16185 in exponential form is:

16185 = 31 × 51 × 131 × 831

Now multiplying the highest exponent prime factors to calculate the LCM of 16172 and 16185.

LCM(16172,16185) = 22 × 131 × 3111 × 31 × 51 × 831
LCM(16172,16185) = 20134140