Question:
The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other?
The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other?
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For any two numbers, HCF × LCM = product. This can quickly find a missing number if HCF, LCM, and one number are known.
Updated On: Aug 1, 2025
- 24
- 48
- 60
72
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The Correct Option is B
Solution and Explanation
- Step 1: Relation between HCF, LCM, and product - For two positive integers $a$ and $b$: \[ \text{HCF}(a,b) \times \text{LCM}(a,b) = a \times b \]
- Step 2: Substitute known values - \[ 12 \times 144 = 36 \times b \]
- Step 3: Solve for $b$ - \[ b = \frac{12 \times 144}{36} = \frac{1728}{36} = 48 \]
- Step 4: Verification - HCF(36, 48) = 12, LCM(36, 48) = $\frac{36 \times 48}{12} = 144$. Both match the given.
- Step 5: Conclusion - The other number is $48$, matching option (2).
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