The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are…

To find the two numbers when you know their Highest Common Factor (H.C.F.) and the remaining co-prime factors of their Least Common Multiple (L.C.M.), you can use a direct multiplication method.

The Concept
If two numbers have an H.C.F. of H, they can be expressed as H * a and H * b, where a and b are co-prime numbers (they share no common factors other than 1). The L.C.M. of these two numbers is H * a * b.

In this problem:

• H.C.F. (H) = 23

• The other two factors of the L.C.M. (which correspond to a and b) = 13 and 14.

Step-by-Step Calculation

1. Find the first number:
   First number = H.C.F. * a = 23 * 13 = 299

2. Find the second number:
   Second number = H.C.F. * b = 23 * 14 = 322

3. Identify the larger number:
   Comparing 299 and 322, the larger number is 322.