Question:
The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other number?
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
- 48
- 60
- 72
- 96
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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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