Question

Hcf of two numbers is 23 and the other two factors of there lcm are 13 and 14 lagrer of two number is

Answer 1

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

[A more detailed explanation ...

we can take the numbers as (23 × 13) and (23 × 14) because of the
following reasons

HCF is given as 23.

The HCF of a group of numbers will be always a factor of their LCM.

Hence, 23 is a factor of the LCM

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

Hence factors of the LCM are 23, 13, 14

Now assume that we take 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 = product of all common prime factors using the least power of each common prime factor

= 23

LCM is the product of highest powers of all prime factors

= 23 × 13 × 2 × 7 = 23 × 13 × 14

Clearly we get HCF as 23 and the factors in the LCM as 13, 14 and 23.

Hence every conditions are satisfied.