Correct Answer - Option 3 : 377
Given:
HCF of two numbers = 29
Other two factors of their LCM = 15 and 13
Concept Used:
The HCF of a group of numbers will be always a factor of their LCM.
HCF is the product of all common prime factors using the least power of each common prime factor.
LCM is the product of the highest powers of all prime factors.
Calculation:
HCF of the two numbers = 29
HCF will be always a factor of LCM.
So, 29 is a factor of the LCM.
Other two factors in the LCM are 13 and 15.
Factors of the LCM are 29, 13 and 15.
So, Numbers can be taken as (29 × 13) and (29 × 15) = 377 and 435
∴ The smallest number is 377.
