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

377

HCF of the two numbers = 29

Since HCF will be always a factor of LCM, 29 is a factor of the LCM.

Given that 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 = 377