Question

The HCF of 2 numbers is 11 and their LCM is 693 If their sum is 176 find the numbers

• A. 99, 77
• B. 110, 66
• C. 88, 77
• D. 121, 44

Answer 1

The correct option is A 99, 77

Let the number are a and b
Then $ab=LCM\times HCF$
$ab=693\times 11$
$ab=7623$
$a=\frac{7623}{b}$
According to the question
$a+b=176$
$\frac{7623}{b}+b=176$
$b^2-176b+7623=0$
$b^2-77b-99b+7623$
$b(b-77)-99(b-77)$
$(b-77)(b-99)$
$b=77or99$
Hence a = 77 or 99
Then the numbers are 77,99.