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If (a=2^4\times3\times5^2) and (b=2^2\times3^3\times5), what is the value of (\frac{\operatorname{LCM}(a,b)}{\operatorname{HCF}(a,b)})?
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Answer and explanation
Correct answer: (2^2\times3^2\times5)
Step 1: LCM uses higher exponents and HCF uses lower exponents. Step 2: In the ratio, subtract exponents: (2^{4-2}\times3^{3-1}\times5^{2-1}=2^2\times3^2\times5). Step 3: Use exponent difference instead of calculating both full numbers.
Frequently asked questions
What is the correct answer to this question?
(2^2\times3^2\times5)
Why is this the correct answer?
Step 1: LCM uses higher exponents and HCF uses lower exponents. Step 2: In the ratio, subtract exponents: (2^{4-2}\times3^{3-1}\times5^{2-1}=2^2\times3^2\times5). Step 3: Use exponent difference instead of calculating both full numbers.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.
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