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What is the smallest number which leaves remainder (0) when divided by (45), (54), and (72)?
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Answer and explanation
Correct answer: (1080)
Step 1: The smallest such number is the LCM of the three numbers. Step 2: (45=3^2\times 5), (54=2\times 3^3), and (72=2^3\times 3^2). The LCM is (2^3\times 3^3\times 5=1080). Step 3: Remainder (0) means exact divisibility by all numbers.
Frequently asked questions
What is the correct answer to this question?
(1080)
Why is this the correct answer?
Step 1: The smallest such number is the LCM of the three numbers. Step 2: (45=3^2\times 5), (54=2\times 3^3), and (72=2^3\times 3^2). The LCM is (2^3\times 3^3\times 5=1080). Step 3: Remainder (0) means exact divisibility by all numbers.
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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