
We are given:
HCF of two numbers = 8
We are asked: Which one of the following options can never be their LCM?
Let’s understand the concept first.
🧠 Key Formula:
HCF×LCM=Product of the two numbers\text{HCF} \times \text{LCM} = \text{Product of the two numbers}
So if HCF = 8, then LCM must be a multiple of 8.
Also, both numbers must be divisible by 8.
🔍 That means:
❌ The LCM can never be a number that is not divisible by 8.
Let’s take sample options to clarify (assuming sample choices like):
A) 24
B) 56
C) 60
D) 120
Now check which of these is not divisible by 8:
24 ÷ 8 = 3 ✅
56 ÷ 8 = 7 ✅
60 ÷ 8 = 7.5 ❌
120 ÷ 8 = 15 ✅
✅ Final Answer:
60 can never be their LCM (since it is not divisible by 8)
Incomplete or missing data is a common challenge in data analysis. Whether it’s skipped survey responses, blank spreadsheet cells, or unavailable values, missing data can affect the accuracy and reliability of your results.
The key is to handle missing data thoughtfully so you can still draw valid conclusions without misleading your interpretation.
—
🔍 Common Ways to Handle Missing Data:
1. Identify the Missing Data
Start by locating where and how much data is missing.
Check: Is it random or following a pattern? Are entire sections missing or just a few values?
2. Remove Incomplete Entries (if appropriate)
If only a small number of rows are missing data, and they don’t heavily impact the dataset, you can safely remove them.
3. Use Imputation (Estimate Missing Values)
If the dataset is large and important, you can fill in missing values using methods like:
– Mean or median substitution (for numerical data)
– Mode (for categorical data)
– Regression or predictive models (for more advanced cases)
4. Use Available Data Only
In some cases, you can perform analysis using just the complete parts of the dataset — as long as it doesn’t bias your results.
5. Flag and Acknowledge Missing Data
Be transparent in reports. Clearly mention how much data is missing and how it was handled.
6. Ask Why the Data Is Missing
Sometimes missing data reveals a deeper issue (e.g., system errors, survey confusion). Understanding the cause can help prevent future problems.
Imagine you’re analyzing survey responses from 1,000 people, but 100 skipped the income question.
Option 1: Exclude those 100 responses if income is critical to your analysis.
Option 2: If income correlates with other known answers (like job title), estimate it using average values for each group.