Question

The HCF of two numbers is 29, and the other two factors of their LCM are 15 and 13. The larger of the two number is:
1. 377
2. 464
3. 406
4. 435

Answer 1

Correct Answer - Option 4 : 435

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.

HCF of the two numbers = 29

Since HCF will be always a factor of LCM, 23 is a factor of the LCM.
Given that the other two factors in the LCM are 15 and 13

Calculation : 

Hence factors of the LCM are 29,13,15

So, numbers can be taken as (29 × 13) and (29 × 15)

Hence, largest number = 435