Question

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
A.276
B.299
C.322
D.345

Answer 1

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

=> Highest Common Factor in the numbers = 23


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

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