The HCF of two numbers is 29, and the other two factors of their LCM are 15 and 13. The larger of the two numbers is:

435

HCF of the two numbers = 29

Since HCF will be always a factor of LCM, 23 is a factor of the LCM.

The other two factors in the LCM are 15 and 13

Hence factors of the LCM are 29,13,15

So, numbers  =  (29 × 13) and (29 × 15)

Hence, largest number = 435