To find the LCM of 12, 15, 20, and 27 using the division method, follow these steps:
### Step 1: Write the numbers in a row
Write down the numbers for which you want to find the LCM:
- 12, 15, 20, 27
### Step 2: Divide by the smallest prime number
Start with the smallest prime number, which is 2. Check which of the numbers are divisible by 2:
- 12 is divisible by 2 (12 ÷ 2 = 6)
- 15 is not divisible by 2 (write it as is)
- 20 is divisible by 2 (20 ÷ 2 = 10)
- 27 is not divisible by 2 (write it as is)
So, we write:
```
2 | 12 15 20 27
| 6 15 10 27
```
### Step 3: Repeat with the next smallest prime number
Now, check the next smallest prime number, which is 3. Divide the results from the previous step:
- 6 is divisible by 3 (6 ÷ 3 = 2)
- 15 is divisible by 3 (15 ÷ 3 = 5)
- 10 is not divisible by 3 (write it as is)
- 27 is divisible by 3 (27 ÷ 3 = 9)
So, we write:
```
3 | 6 15 10 27
| 2 5 10 9
```
### Step 4: Continue with the next prime number
Next, we will use 3 again:
- 2 is not divisible by 3 (write it as is)
- 5 is not divisible by 3 (write it as is)
- 10 is not divisible by 3 (write it as is)
- 9 is divisible by 3 (9 ÷ 3 = 3)
So, we write:
```
3 | 2 5 10 9
| 2 5 10 3
```
### Step 5: Continue dividing by 3
Now, we will divide by 3 again:
- 2 is not divisible by 3 (write it as is)
- 5 is not divisible by 3 (write it as is)
- 10 is not divisible by 3 (write it as is)
- 3 is divisible by 3 (3 ÷ 3 = 1)
So, we write:
```
3 | 2 5 10 3
| 2 5 10 1
```
### Step 6: Divide by 5
Now, we will divide by the next prime number, which is 5:
- 2 is not divisible by 5 (write it as is)
- 5 is divisible by 5 (5 ÷ 5 = 1)
- 10 is divisible by 5 (10 ÷ 5 = 2)
- 1 is not divisible by 5 (write it as is)
So, we write:
```
5 | 2 5 10 1
| 2 1 2 1
```
### Step 7: Write down the LCM
Now, we have reached all 1s. To find the LCM, we multiply all the prime numbers used in the division:
- LCM = 2 × 2 × 3 × 3 × 5 = 4 × 3 = 12 × 3 = 36 × 5 = 180
### Final Answer
The LCM of 12, 15, 20, and 27 is **180**.
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