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If two positive integers p and q are written as p = a3b4 and q = a4b4, where a and b are prime numbers,then LCM (p, q) × HCF (p, q) is :
- a)a7b6
- b)a6b7
- c)a8b7
- d)a7b8
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If two positive integers p and q are written as p = a3b4 and q = a4b4,...
p = a3b4
and q = a4b4
Then LCM (p, q) = a4 b4
and HCF (p, q) = a3 b4
∴ LCM (p, q) x HCF (p, q)
= a4 b4 x a3 b4
= a7 b8
and q = a4b4
Then LCM (p, q) = a4 b4
and HCF (p, q) = a3 b4
∴ LCM (p, q) x HCF (p, q)
= a4 b4 x a3 b4
= a7 b8
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Community Answer
If two positive integers p and q are written as p = a3b4 and q = a4b4,...
To find the least common multiple (LCM) of p and q, we need to find the highest power of each prime factor that appears in either p or q.
In this case, we have p = a^3 * b^4 and q = a^4 * b^4.
The prime factor a appears with a higher power in q (a^4) than in p (a^3), so we take the higher power of a, which is a^4.
The prime factor b appears with the same power in both p and q (b^4), so we can simply take b^4.
Therefore, the LCM of p and q is a^4 * b^4.
In this case, we have p = a^3 * b^4 and q = a^4 * b^4.
The prime factor a appears with a higher power in q (a^4) than in p (a^3), so we take the higher power of a, which is a^4.
The prime factor b appears with the same power in both p and q (b^4), so we can simply take b^4.
Therefore, the LCM of p and q is a^4 * b^4.
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If two positive integers p and q are written as p = a3b4 and q = a4b4, where a and b are prime numbers,then LCM (p, q) × HCF (p, q) is :a)a7b6b)a6b7c)a8b7d)a7b8Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If two positive integers p and q are written as p = a3b4 and q = a4b4, where a and b are prime numbers,then LCM (p, q) × HCF (p, q) is :a)a7b6b)a6b7c)a8b7d)a7b8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two positive integers p and q are written as p = a3b4 and q = a4b4, where a and b are prime numbers,then LCM (p, q) × HCF (p, q) is :a)a7b6b)a6b7c)a8b7d)a7b8Correct answer is option 'D'. Can you explain this answer?.
If two positive integers p and q are written as p = a3b4 and q = a4b4, where a and b are prime numbers,then LCM (p, q) × HCF (p, q) is :a)a7b6b)a6b7c)a8b7d)a7b8Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If two positive integers p and q are written as p = a3b4 and q = a4b4, where a and b are prime numbers,then LCM (p, q) × HCF (p, q) is :a)a7b6b)a6b7c)a8b7d)a7b8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two positive integers p and q are written as p = a3b4 and q = a4b4, where a and b are prime numbers,then LCM (p, q) × HCF (p, q) is :a)a7b6b)a6b7c)a8b7d)a7b8Correct answer is option 'D'. Can you explain this answer?.
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