If the HCF of two numbers (each greater than 17) is 17 and the LCM is 561, then find the sum of the numbers.

If the HCF of two numbers (each greater than 17) is 17 and the LCM is 561.

Let's assume the numbers are 17a and 17b respectively.

$$Product\ of\ these\ two\ number\ =\ LCM\times\ HCF$$

$$17a\times17b\ =\ 561\times17$$

$$a\times b\ =\ 3\times11$$      [Here the values of a and b will not be 1 and 33. Because each of the numbers should be greater than 17.]

so the values of 'a' and 'b' will be 3 and 11.

Sum of the numbers = 17a+17b

= 17(a+b)

= 17(3+11)

= $$17\times14$$

= 238