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📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Solution: The prime factorization is already given: $ 2^4 \cdot 3^3 \cdot 5^2 $. The largest prime factor is clearly $ \boxed{5} $.

📌 Question: What is the smallest positive integer divisible by both 12 and 18?

📌 Solution: To find the least common multiple of 12 and 18, factor both:

📌 $ 12 = 2^2 \cdot 3 $

📌 $ 18 = 2 \cdot 3^2 $

📌 Take the maximum exponent for each prime:

📌 $ 2^2 $, $ 3^2 $

📌 So, LCM is $ 2^2 \cdot 3^2 = 4 \cdot 9 = 36 $.

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The product of two consecutive even integers is 168. Find the smaller...
Let integers: \(x\) and \(x + 2\)
\(x(x + 2) = 168 \Rightarrow x^2 + 2x - 168 = 0\)
Discriminant: \(4 + 672 = 676 = 26^2\)
\(x = \frac{-2 \pm 26}{2} \Rightarrow x = 12\) or \(x = -14\)
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A circle is inscribed in a square with side length 10 cm. What is the...
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Shaded area: \(100 - 25\pi\) cm²

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