Question

If the sum of two numbers is 27 and their hcf and lcm are 3 and 60

Answer 1

Let the no. be a and b

• a + b = 27

a = 27 - b .....( i )

Since ,

HCF × LCM = product of two nos.

3 × 60 = ab

180 = ab .....( ii )

Putting in ( ii ) value of a from ( i )

ab = 180

( 27 - b ) b = 180

27b - b² = 180

b² - 27b + 180 = 0

b² - 12b - 15b + 180 = 0

b ( b - 12 ) - 15 ( b - 15 ) = 0

( b - 12 ) ( b - 15 ) = 0


• ( b - 12 ) = 0
b = 12


• ( b - 15 ) = 0
b = 15

If we take b = 12

a = 27 - b

a = 27 - 12

a = 15



If we take b = 15

a = 27 - b

a = 12