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If a number leaves remainder (17) when divided by (64), (80), and (96), what is the smallest such number?
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Answer and explanation
Correct answer: (977)
Step 1: Subtracting (17) makes the number divisible by all three numbers. Step 2: (64=2^6), (80=2^4\times5), and (96=2^5\times3), so the LCM is (960). Hence the number is (960+17=977). Step 3: Add the common remainder at the end.
Frequently asked questions
What is the correct answer to this question?
(977)
Why is this the correct answer?
Step 1: Subtracting (17) makes the number divisible by all three numbers. Step 2: (64=2^6), (80=2^4\times5), and (96=2^5\times3), so the LCM is (960). Hence the number is (960+17=977). Step 3: Add the common remainder at the end.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: HCF and LCM using prime factorisation.
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