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If p, q and r are positive integers such that pq=231 and qr=63 then the smallest possible value of p+q+r is?
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If p, q and r are positive integers such that pq=231 and qr=63 then th...
Solution:


Given:


  • pq = 231

  • qr = 63

  • p, q, r are positive integers



To find:


  • The smallest possible value of pqr



Approach:


  • Firstly, we need to factorize 231 and 63 to get the values of p, q and r.

  • Then, we need to find the product of p, q and r to get the smallest possible value of pqr.



Factorizing 231:


  • 231 can be factorized as 231 = 3 × 7 × 11.

  • Therefore, p, q and r can take the values of 3, 7 and 11 in some order.



Factorizing 63:


  • 63 can be factorized as 63 = 3 × 3 × 7.

  • Therefore, p, q and r can take the values of 3, 7 and 3 in some order.



Product of p, q and r:


  • The possible values of p, q and r are:


    • p = 3, q = 7, r = 11

    • p = 3, q = 11, r = 7

    • p = 7, q = 3, r = 3

    • p = 11, q = 3, r = 7


  • The product of p, q and r for each of the above cases is:


    • 3 × 7 × 11 = 231

    • 3 × 11 × 7 = 231

    • 7 × 3 × 3 = 63

    • 11 × 3 × 7 = 231


  • Therefore, the smallest possible value of pqr is 63.



Answer:


  • The smallest possible value of pqr is 63.

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If p, q and r are positive integers such that pq=231 and qr=63 then the smallest possible value of p+q+r is?
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