Correct Answer - Option 1 : 728
Given:
Ratio of two numbers = 7 : 13
HCF = 8
Concept used:
(i) If a and b are two numbers, then a × b = HCF × LCM
(ii) HCF of two numbers is the highest common factor of both of them.
Calculations:
Let the numbers be 7x and 13x.
Then, H.C.F. = x
As we have given, x = 8
First number is,
⇒ 7x
⇒ 7 × 8 = 56
Second number is,
⇒ 13x
⇒ 13 × 8 = 104
a × b = HCF × LCM
⇒ 56 × 104 = 8 × LCM
⇒ LCM = 728
∴ The LCM is 728.
