The HCF of the two numbers is 29 & their sum is 174 the possible numbers are

Answer: Option B

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 = 23Since 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, 14So, numbers can be taken as (23 × 13) and (23 × 14)= 299 and 322

Hence, largest number = 322

We have seen that the numbers are (23 × 13) and (23 × 14).If we write the numbers as the product of prime factors,first number = (23 × 13)second numbers = (23 × 14) = (23 × 2 × 7)HCF is the product of all common prime factors using the least power of each common prime factor= 23LCM is the product of highest powers of all prime factors= 23 × 13 × 2 × 7 = 23 × 13 × 14Clearly we get HCF as 23 and the factors in the LCM as 13, 14 and 23.

Hence every conditions are satisfied.

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The HCF of two numbers is 29 and their LCM is 1160. If one of the numbers is 145 , find the other.

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