Sure, let's break down the problem step by step to find the required values and then calculate the sum.
### Step 1: Calculate the Highest Common Factor (HCF) of 120 and 108
The HCF of two numbers is the largest number that divides both of them without leaving a remainder. For the numbers 120 and 108, the HCF is 12.
### Step 2: Calculate the Least Common Multiple (LCM) of 120 and 108
The LCM of two numbers is the smallest number that is a multiple of both. We can find the LCM using the relationship between HCF and LCM:
[tex]\[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{HCF}(a, b)} \][/tex]
Substituting the values:
[tex]\[ \text{LCM}(120, 108) = \frac{|120 \times 108|}{\text{HCF}(120, 108)} = \frac{12960}{12} = 1080 \][/tex]
### Step 3: Given Values
We are given two additional values:
- HCFOF: 45
- IOS: 900
### Step 4: Calculate the Sum
We need to find the sum of the HCF of 120 and 108, the LCM of 120 and 108, HCFOF, and IOS.
So, we sum up all these values:
[tex]\[ \text{Sum} = \text{HCF} + \text{LCM} + \text{HCFOF} + \text{IOS} \][/tex]
[tex]\[ \text{Sum} = 12 + 1080 + 45 + 900 \][/tex]
[tex]\[ \text{Sum} = 2037 \][/tex]
### Final Answer
The values are:
- HCF of 120 and 108: 12
- LCM of 120 and 108: 1080
- Sum of HCF, LCM, HCFOF, and IOS: 2037
So, the final answer is:
[tex]\[ (12, 1080, 2037) \][/tex]
