Find the LCM of 125, 350 and 245 by common division method.

Answer

To find the LCM of 125, 350, and 245 using the common division method, we follow these steps:

### Step 1: Write the numbers in a row
We start by writing the numbers we need to find the LCM for:
- 125
- 350
- 245

### Step 2: Divide by the smallest prime number
We begin dividing the numbers by the smallest prime number that can divide at least one of the numbers. The smallest prime number is 5.
- 125 ÷ 5 = 25
- 350 ÷ 5 = 70
- 245 ÷ 5 = 49

Now we write the results below:
```
125 350 245
-----------------
5 25 70 49
```

### Step 3: Continue dividing
Next, we look for the next smallest prime number that can divide any of the results. The next prime number is 7.
- 25 cannot be divided by 7, so it remains 25.
- 70 ÷ 7 = 10
- 49 ÷ 7 = 7

Now we write the results below:
```
125 350 245
-----------------
5 25 70 49
7 25 10 7
```

### Step 4: Continue dividing until all numbers are 1
Next, we divide by the next prime number, which is 2.
- 25 cannot be divided by 2, so it remains 25.
- 10 ÷ 2 = 5
- 7 cannot be divided by 2, so it remains 7.

Now we write the results below:
```
125 350 245
-----------------
5 25 70 49
7 25 10 7
2 25 5 7
```

Finally, we divide by 5:
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
- 7 remains 7.

Now we write the results below:
```
125 350 245
-----------------
5 25 70 49
7 25 10 7
2 25 5 7
5 5 1 7
```

### Step 5: Write down the prime factors
Now we take all the prime numbers we used for division:
- 5 (from the first division)
- 7 (from the second division)
- 2 (from the third division)
- 5 (from the last division)

### Step 6: Calculate the LCM
Now, we multiply all the prime factors together:
LCM = 5 × 5 × 7 × 5 × 7 × 2

Calculating this step-by-step:
1. 5 × 5 = 25
2. 25 × 7 = 175
3. 175 × 5 = 875
4. 875 × 7 = 6125
5. 6125 × 2 = 12250

So, the LCM of 125, 350, and 245 is **12250**.