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If (m=2^3\times3^a\times5^2) and (n=2^5\times3^2\times5^b\times11) have LCM (2^5\times3^6\times5^4\times11), which values are correct?
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Answer and explanation
Correct answer: (a=6), (b=4)
Step 1: LCM uses the highest power of each prime. Step 2: The highest power of (3) must be (6), so (a=6); the highest power of (5) must be (4), so (b=4). Step 3: In unknown-power LCM questions, identify the maximum power.
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What is the correct answer to this question?
(a=6), (b=4)
Why is this the correct answer?
Step 1: LCM uses the highest power of each prime. Step 2: The highest power of (3) must be (6), so (a=6); the highest power of (5) must be (4), so (b=4). Step 3: In unknown-power LCM questions, identify the maximum power.
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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