Question

what is the lcm of 115,161 and 299

Answer 1

$lcm(115,161,299)$ - less common multiple

It is easy to confirm that

115=5*23

161=7*23

299=13*23

According to the theorem about factorization of natural value

$$\left. \begin{array}{l} a = p _ {1} ^ {q _ {1}} p _ {2} ^ {q _ {2}} \dots p _ {r _ {1}} ^ {q _ {r _ {1}}} \\ b = p _ {1} ^ {t _ {1}} p _ {2} ^ {t _ {2}} \dots p _ {r _ {1}} ^ {t _ {r _ {2}}} \\ c = p _ {1} ^ {l _ {1}} p _ {2} ^ {l _ {2}} \dots p _ {r _ {1}} ^ {l _ {r _ {2}}} \end{array} \right\} \Rightarrow l c m (a, b, c) = p _ {1} ^ {\max \{q _ {1}, t _ {1}, l _ {1} \}} p _ {2} ^ {\max \{q _ {2}, t _ {2}, l _ {2} \}} \dots - \text {the definition}.$$

As we can manually calculate

$$p _ {1} = 5, p _ {2} = 7, p _ {3} = 1 3, p _ {4} = 2 3. \max _ {r, l, t} \left\{q _ {i}, t _ {i}, l _ {i} \right\} = 1 \Rightarrow$$

Consequently, according to the definition

$lcm(115,161,299) = 5\cdot 7\cdot 13\cdot 23 = 10465$