Find the LCM of 12, 20 and 36 by division method

Answer

To find the LCM (Least Common Multiple) of 12, 20, and 36 using the division method, follow these steps:

### Step 1: Write the numbers in a row
We start by writing the numbers we want to find the LCM for:
- 12
- 20
- 36

### Step 2: Divide by the smallest prime number
We look for the smallest prime number that can divide at least one of the numbers. The smallest prime number is 2.
- 12 ÷ 2 = 6
- 20 ÷ 2 = 10
- 36 ÷ 2 = 18

Now we write the results below:
```
12 20 36
2
6 10 18
```

### Step 3: Repeat the process
Now we check if we can divide again by the smallest prime number. We can divide by 2 again:
- 6 ÷ 2 = 3
- 10 ÷ 2 = 5
- 18 ÷ 2 = 9

Now we write the results below:
```
12 20 36
2
6 10 18
2
3 5 9
```

### Step 4: Continue until all numbers are prime
Now we look at the numbers 3, 5, and 9. The smallest prime number that can divide at least one of these is 3:
- 3 ÷ 3 = 1
- 5 ÷ 5 = 1
- 9 ÷ 3 = 3

Now we write the results below:
```
12 20 36
2
6 10 18
2
3 5 9
3
1 1 3
```

### Step 5: Write down the prime factors
Now we have reached 1 for two of the numbers. The last row shows the prime factors used for division:
- The prime factors are 2, 2, 3, 5, and 3.

### Step 6: Calculate the LCM
To find the LCM, we multiply all the prime factors together:
- LCM = 2 × 2 × 3 × 5 × 3

Calculating this:
- 2 × 2 = 4
- 4 × 3 = 12
- 12 × 5 = 60
- 60 × 3 = 180

So, the LCM of 12, 20, and 36 is **180**.

### Summary
The LCM of 12, 20, and 36 is **180**.

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