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:

The problem states that we have two numbers. One of them is 23 and the other is unknown. The LCM of these two numbers has additional factors of 13 and 14.

Step 1: Understand the problem The LCM (Least Common Multiple) of two numbers is the smallest multiple that is exactly divisible by every one of the numbers. Since 23 is a prime number, the LCM of 23 and the unknown number is simply 23 multiplied by the unknown number.

Step 2: Identify the factors of the LCM The problem states that the LCM has additional factors of 13 and 14. This means that the LCM is a multiple of 13, 14, and 23.

Step 3: Calculate the LCM Since the LCM is a multiple of 13, 14, and 23, we can calculate it by multiplying these three numbers together. 13 * 14 * 23 = 4162

Step 4: Find the unknown number Since the LCM of 23 and the unknown number is 4162, we can find the unknown number by dividing the LCM by 23. 4162 / 23 = 181

So, the larger of the two numbers is 181.