Question

M and n are two natural numbers such that m+n=949. lcm of m and n is 2628 what is the hcf of m and n select one:



a. 23



b. none of these



c. 69

Answer 1

hello friend here's your answer

it's option C. 69

hope that this helps you.....

Answer 2

As we know, the two numbers are m and n.

Given: The LCM of two natural numbers such as m and n is 2628 and the sum of the number is 949 $m+n=949$.

$949=73\times 13$

$2628=73\times 3^2\times 2^2$

Hence, the HCF of 949 and 2628 is 73.

Therefore the sum of two numbers m and n is written as,

$73a+73b=949$

      $a+b=13$

      $a-b=\sqrt{(a+b)^2-4ab}\\a-b=\sqrt{(13)^2-144}\\a-b=\sqrt{169-144}\\a-b=5$

Hence a and b are 9 and 4.

$m=73a\\m=73\times 9\\m=657$

$n=73b\\n=73\times 4\\n=292$

The two numbers m and n are 657 and 292.

HCF of m and n  is 73.

Option B is correct.

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