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Two numbers are (2^a\times 3\times 5^2) and (2^2\times 3^4\times 5^b). If their LCM is (2^5\times 3^4\times 5^3), what is ((a,b))?
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Answer and explanation
Correct answer: ((5,3))
Step 1: LCM takes the greater exponents. Step 2: For (2), (\max(a,2)=5), so (a=5). For (5), (\max(2,b)=3), so (b=3). Step 3: To match an LCM, compare the required largest exponents.
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What is the correct answer to this question?
((5,3))
Why is this the correct answer?
Step 1: LCM takes the greater exponents. Step 2: For (2), (\max(a,2)=5), so (a=5). For (5), (\max(2,b)=3), so (b=3). Step 3: To match an LCM, compare the required largest exponents.
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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