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The HCF of two numbers is (30) and their LCM is (2730). How many unordered pairs of such numbers are possible?
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Answer and explanation
Correct answer: (2)
Step 1: Let the numbers be (30m) and (30n), where (m) and (n) are coprime. Step 2: (30mn=2730), so (mn=91=7\times13); the unordered coprime pairs are ((1,91)) and ((7,13)). Step 3: Do not count reversed order as a new pair.
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What is the correct answer to this question?
(2)
Why is this the correct answer?
Step 1: Let the numbers be (30m) and (30n), where (m) and (n) are coprime. Step 2: (30mn=2730), so (mn=91=7\times13); the unordered coprime pairs are ((1,91)) and ((7,13)). Step 3: Do not count reversed order as a new pair.
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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