Question

7. If the H.C.F. of two numbers (each greater
than 13) be 13 and L.C.M. 273, then the sum
of the numbers will be
(S.S.C. 2006)​

Answer 1

ANSWER = 39 , 91 or 91 , 31

$\huge\mathfrak\red{Question}$

HCF of two numbers is 13 and LCM is 273 each number is greater than 13

$\huge\mathfrak\orange{ to \: find }$

• The sum of numbers

$\huge\mathfrak\green{ Answer }$

Let the numbers be 'p' and 'q'

HCF = 13

$p = 13 a$

$q = 13 b$

$LCM = 273$

$13 ab = 273$

$ab = \frac{273 }{ 13 }$

$= 21$

$13 a > 13 , a > 1$

$13 b > 13 , b > 1$

$ab = 21$

$factors \: of \:21 = 1 , 3 , 7 , 21$

• among this 21 and 1 will not be the value ,

that is

values are 3 and 7

$13 a = 13 × 3 = 39$

$13 b = 13 × 7 = 91$

numbers are (39, 91) or (91 , 39)