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If (A=2^2\times5^3) and (B=2^4\times3^2\times5), how many factors will the LCM of (A) and (B) have?
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Answer and explanation
Correct answer: (45)
Step 1: LCM takes the highest exponent of every prime factor. Step 2: LCM (=2^4\times3^2\times5^3). Total factors (=(4+1)(2+1)(3+1)=5\times3\times4=60). Step 3: After finding the LCM, apply the factor-count rule.
Frequently asked questions
What is the correct answer to this question?
(45)
Why is this the correct answer?
Step 1: LCM takes the highest exponent of every prime factor. Step 2: LCM (=2^4\times3^2\times5^3). Total factors (=(4+1)(2+1)(3+1)=5\times3\times4=60). Step 3: After finding the LCM, apply the factor-count rule.
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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