The LCM of 88 and 220 is :
A)220
B)1100
C)440
D)880

Options

A. 220
B. 1100
C. 440
D. 880

Answer

To find the LCM (Least Common Multiple) of 88 and 220, we will follow these steps:

### Step 1: Prime Factorization of 88
First, we need to find the prime factorization of 88.
- 88 can be divided by 2:
- 88 ÷ 2 = 44
- 44 ÷ 2 = 22
- 22 ÷ 2 = 11
- 11 is a prime number.

So, the prime factorization of 88 is:
\[ 88 = 2^3 \times 11^1 \]

### Step 2: Prime Factorization of 220
Next, we will find the prime factorization of 220.
- 220 can also be divided by 2:
- 220 ÷ 2 = 110
- 110 ÷ 2 = 55
- 55 can be divided by 5:
- 55 ÷ 5 = 11
- 11 is a prime number.

So, the prime factorization of 220 is:
\[ 220 = 2^2 \times 5^1 \times 11^1 \]

### Step 3: Identify the Maximum Powers of Each Prime Factor
To find the LCM, we take the highest power of each prime factor from both numbers:
- For the prime factor 2:
- From 88, we have \( 2^3 \)
- From 220, we have \( 2^2 \)
- Maximum power is \( 2^3 \)

- For the prime factor 5:
- From 88, we have \( 5^0 \) (since 5 is not a factor of 88)
- From 220, we have \( 5^1 \)
- Maximum power is \( 5^1 \)

- For the prime factor 11:
- From both 88 and 220, we have \( 11^1 \)
- Maximum power is \( 11^1 \)

### Step 4: Calculate the LCM
Now we can calculate the LCM using the maximum powers:
\[ \text{LCM} = 2^3 \times 5^1 \times 11^1 \]
Calculating this step by step:
- \( 2^3 = 8 \)
- \( 5^1 = 5 \)
- \( 11^1 = 11 \)

Now multiply:
\[ 8 \times 5 = 40 \]
Then multiply by 11:
\[ 40 \times 11 = 440 \]

Thus, the LCM of 88 and 220 is:
\[ \text{LCM} = 440 \]

### Final Answer:
The LCM of 88 and 220 is **C) 440**.

---