Question

The HCF of two numbers is 29 and other two factores of thier LCM is 16 and 19. Find the larger of two numbers.​

Answer 1

Answer:

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Step-by-step explanation:

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 highest powers of all prime factors.

HCF of the two numbers = 23

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

Given that other two factors in the LCM are 13 and 14.

Hence factors of the LCM are 23, 13, 14

So, numbers can be taken as (23 × 13) and (23 × 14)

= 299 and 322

Hence, largest number = 322