Correct Answer - Option 3 : 156
Given:
HCF = 13
One number = 117
Concept Used:
Number 1 = HCF× (a)
Number 2 = HCF× (b)
Calculation:
Let the ratio of two numbers be a : b
here 'a' and 'b' are co-prime numbers.
1st number = 117 and HCF = 13
⇒ 117 = 13 × a
⇒ a = 9
Now b will be a co-prime number of 9
Now comparing with the options,
Option 1 = 169
⇒ 169 = 13 × b
⇒ b = 13
9 and 13 are co-prime numbers.
Hence the second number can be = 169
Now option 2 =143
⇒ 143 = 13 × b
⇒ b = 11
9 and 11 are co-prime numbers.
Hence the second number can be = 143
Now option 4 = 130
⇒ 130 = 13 × b
⇒ b = 10
9 and 10 are co-prime numbers.
Now option 3 = 156
⇒ 156 = 13 × b
⇒ b = 12
9 and 12 are not co-prime numbers.
∴ 156 cannot be a second number.