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A number leaves remainder (0) when divided by (144), (180), and (216). What is the smallest such number?
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Answer and explanation
Correct answer: (2160)
Step 1: Remainder (0) means the number is exactly divisible by all three numbers. Step 2: (144=2^4\times3^2), (180=2^2\times3^2\times5), and (216=2^3\times3^3), so LCM (=2^4\times3^3\times5=2160). Step 3: For the smallest divisible number, find the LCM.
Frequently asked questions
What is the correct answer to this question?
(2160)
Why is this the correct answer?
Step 1: Remainder (0) means the number is exactly divisible by all three numbers. Step 2: (144=2^4\times3^2), (180=2^2\times3^2\times5), and (216=2^3\times3^3), so LCM (=2^4\times3^3\times5=2160). Step 3: For the smallest divisible number, find the 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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