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:Choices:- 276 299 322 345

The Highest Common Factor (HCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the HCF is given as 23.

The Lowest Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both of them. In this case, the other two factors of the LCM are given as 13 and 14.

Since the HCF is a factor of the LCM, we can find the LCM by multiplying the HCF and the other two factors together.

So, LCM = HCF * other factor 1 * other factor 2 = 23 * 13 * 14 = 4162

The two numbers are factors of the LCM, so they must be divisors of 4162. The possible pairs of divisors are (1, 4162), (2, 2081), (13, 320), (23, 181), (26, 160), (46, 90), (322, 13), and (276, 15).

The only pairs that include the HCF 23 are (23, 181) and (46, 90). However, 181 and 90 are not multiples of 23, so they cannot be the numbers we are looking for.

The only pair that includes multiples of 23 is (322, 13). Therefore, the two numbers are 322 and 299 (23*13), and the larger of the two numbers is 322.

So, the correct answer is 322.