Two number, both greater than 29, have GCD = 29 and LCM = 4147. The sum of the numbers is:

  • Option 1)

    669

  • Option 2)

    696

  • Option 3)

    766

  • Option 4)

    767

  • Option 5)

    -

Answers (1)

Product \: of\: numbers = 29\ast 4147.

Let \: the\: numbers \: be 29a \: and\: 29b.\:

Then, 29a \ast 29b = \left ( 24\ast 4147 \right )

=> ab = 143.

Now,\: co-primes \: with\: product \: 143 \:are \:\left ( 1, 143 \right ) \:and \:\left ( 11, 13 \right ).

So, \:the\: numbers\: are\: \left ( 29 \ast 1, 29\ast 143 \right )\:and\:\left ( 29 \ast 11, 29\ast 13 \right )

Since \: both \: numbers\: are \: greater\: than\: 29,

\: the\: suitable\: pair \: is \: \left ( 29 \ast 11, 29 \ast 13 \right )

i.e., \left ( 319, 377 \right ).

Required\: sum = \left ( 319 + 377 \right ) = 696.

 

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