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What is the smallest number that leaves remainder (0) when divided by (45), (60), and (75)?
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Answer and explanation
Correct answer: (900)
Step 1: Remainder (0) means the number is divisible by all the given numbers. Step 2: (45=3^2\times5), (60=2^2\times3\times5), and (75=3\times5^2), so LCM (=2^2\times3^2\times5^2=900). Step 3: For the smallest such number, use LCM.
Frequently asked questions
What is the correct answer to this question?
(900)
Why is this the correct answer?
Step 1: Remainder (0) means the number is divisible by all the given numbers. Step 2: (45=3^2\times5), (60=2^2\times3\times5), and (75=3\times5^2), so LCM (=2^2\times3^2\times5^2=900). Step 3: For the smallest such number, use LCM.
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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