Question:

The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other number?

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Use the formula $a \times b = \text{HCF} \times \text{LCM}$ to find the second number when HCF, LCM, and one number are given.
Updated On: Jul 28, 2025
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The Correct Option is A

Solution and Explanation


- Step 1: Let the two numbers be $a$ and $b$, with $a = 36$. Given HCF = 12 and LCM = 144.
- Step 2: Use the relation: $a \times b = \text{HCF} \times \text{LCM}$.
- Step 3: Substitute: $36 \times b = 12 \times 144$.
- Step 4: Calculate: $36b = 1728$, so $b = \dfrac{1728}{36} = 48$.
- Step 5: Verify: HCF of 36 and 48 is 12 (factors check); LCM is $36 \times 48 \div 12 = 144$.
- Step 6: Check options: Option (a) is 48, which matches.
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