The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. The larger of the two numbers is:

(a) 276

(b) 299

(c) 322

(d) 345

The LCM (Least Common Multiple) of two numbers a and b is the smallest number which is exactly divisible by both the numbers a and b.

Answer: c) 322

HCF(Highest Common Factor) of a and b is the highest number that divides a and b exactly leaving the remainder 0.

Explanation:

If the HCF of the two numbers is 23, then let the two numbers be 23x and 23y.

The LCM of these two numbers can be written as 23xy.

Since the other two factors of LCM are 13 and 14, therefore the values of x and y are 13 and 14 respectively.

So, the largest number is 23y,

23y = 23 × 14 = 322

Therefore, the correct option is (c) 322