Find the L.C.M. of the given numbers by division method:
(i) 48, 60 `" "` (ii) 112, 168, 266.

Answer

To find the L.C.M. (Least Common Multiple) of the given numbers using the division method, we will follow these steps for both parts of the question.

### Part (i): Find the L.C.M. of 48 and 60

**Step 1: Write the numbers in a row.**
- We have 48 and 60.

**Step 2: Divide by the smallest prime factor.**
- The smallest prime factor that divides both numbers is 2.
- Divide both numbers by 2:
- 48 ÷ 2 = 24
- 60 ÷ 2 = 30

**Step 3: Write the results below.**
```
48 60
------
2 | 24 30
```

**Step 4: Repeat the process.**
- Now, we can again divide by 2 since both 24 and 30 are even.
- Divide both numbers by 2:
- 24 ÷ 2 = 12
- 30 ÷ 2 = 15
```
48 60
------
2 | 24 30
2 | 12 15
```

**Step 5: Continue dividing.**
- Now, 12 is divisible by 2, but 15 is not. So we divide 12 by 2:
- 12 ÷ 2 = 6
- 15 remains the same.
```
48 60
------
2 | 24 30
2 | 12 15
2 | 6 15
```

**Step 6: Divide again.**
- Now, 6 is divisible by 2 and 15 remains the same:
- 6 ÷ 2 = 3
```
48 60
------
2 | 24 30
2 | 12 15
2 | 6 15
2 | 3 15
```

**Step 7: Now divide by 3.**
- Now, 3 and 15 are both divisible by 3:
- 3 ÷ 3 = 1
- 15 ÷ 3 = 5
```
48 60
------
2 | 24 30
2 | 12 15
2 | 6 15
2 | 3 15
3 | 1 5
```

**Step 8: Finally, divide by 5.**
- 5 is a prime number:
- 5 ÷ 5 = 1
```
48 60
------
2 | 24 30
2 | 12 15
2 | 6 15
2 | 3 15
3 | 1 5
5 | 1 1
```

**Step 9: Write down the L.C.M.**
- The L.C.M. is the product of all the prime factors used in the division:
- L.C.M. = 2 × 2 × 2 × 3 × 5 = 240

### Part (ii): Find the L.C.M. of 112, 168, and 266

**Step 1: Write the numbers in a row.**
- We have 112, 168, and 266.

**Step 2: Divide by the smallest prime factor.**
- The smallest prime factor that divides all three numbers is 2.
- Divide:
- 112 ÷ 2 = 56
- 168 ÷ 2 = 84
- 266 ÷ 2 = 133
```
112 168 266
------
2 | 56 84 133
```

**Step 3: Repeat the process.**
- Now, 56 and 84 are even, so we divide by 2 again:
- 56 ÷ 2 = 28
- 84 ÷ 2 = 42
- 133 remains the same.
```
112 168 266
------
2 | 56 84 133
2 | 28 42 133
```

**Step 4: Continue dividing.**
- 28 and 42 are even, divide by 2 again:
- 28 ÷ 2 = 14
- 42 ÷ 2 = 21
```
112 168 266
------
2 | 56 84 133
2 | 28 42 133
2 | 14 21 133
```

**Step 5: Divide by 7.**
- Now, we can divide by 7 since 21 is divisible by 7:
- 14 ÷ 2 = 7
- 21 ÷ 7 = 3
- 133 remains the same.
```
112 168 266
------
2 | 56 84 133
2 | 28 42 133
2 | 14 21 133
2 | 7 3 133
```

**Step 6: Divide by 3.**
- Now, we can divide by 3:
- 3 ÷ 3 = 1
```
112 168 266
------
2 | 56 84 133
2 | 28 42 133
2 | 14 21 133
2 | 7 3 133
3 | 1 7 133
```

**Step 7: Divide by 19.**
- Finally, we can divide by 19:
- 133 ÷ 19 = 7
```
112 168 266
------
2 | 56 84 133
2 | 28 42 133
2 | 14 21 133
2 | 7 3 133
3 | 1 7 133
19 | 1 1
```

**Step 8: Write down the L.C.M.**
- The L.C.M. is the product of all the prime factors used in the division:
- L.C.M. = 2 × 2 × 2 × 7 × 3 × 19 = 4032

### Final Answers:
- L.C.M. of 48 and 60 is **240**.
- L.C.M. of 112, 168, and 266 is **4032**.