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:

Answer 1

Hcf=23
Other two factors of lcm =13 and 14
Since hcf is a factor of lcm
Therefore lcm=23 * 13*14
Therefore the two nos are
23*13=299
23*14=322
The larger of the two=322

Answer 2

Answer:

The largest number is 322.

Correct Question :

The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. What is the largest number?

Solution :

______________________________________

Given that :

The HCF of two numbers is 23.

The other two factorsof their LCM are 13 and 14.

To find :

The largest number.

Solution :

As given,

Highest Common Factor in the numbers = 23

So,

23 is a factor of the LCM.  

∵ The HCF always will be the factor of the LCM.

The other two factors in the LCM are 13 and 14.

∴ The factors of the LCM are 23, 13, 14.

Now,

Number can be taken as :

⇒ 23 × 13

⇒ 299

⇒ 23 × 14

⇒ 322

Therefore,

We get two numbers :

299

322

So,

⇒ 299 < 322

∴ The number given answer is 322.