Match List -I with List -II and select the correct answer using the codes given below the lists :
`{:(,"List-I (Numbers)","List -II(TheirLCM)"),(A.,"12,80,20",1.48),(B.,"12,16,24","2.240"),(C.,"5,18,20","3.180"),(D.,"18,24,56","4.504"):}`
Codes :
`{:(,A,B,C,D),((a),3,2,4,1),((b),2,1,3,4),((c ),3,4,2,1),((d),3,1,2,4):}`

Answer

To solve the problem of matching the numbers in List-I with their corresponding LCMs in List-II, we will calculate the LCM for each set of numbers in List-I step by step.

### Step 1: Calculate LCM of 12, 80, and 20 (Option A)
1. **Prime Factorization**:
- 12 = 2² × 3
- 80 = 2⁴ × 5
- 20 = 2² × 5

2. **Identify the highest powers of each prime**:
- For 2: max(2², 2⁴, 2²) = 2⁴
- For 3: max(3¹) = 3¹
- For 5: max(5¹) = 5¹

3. **Calculate LCM**:
\[ \text{LCM} = 2⁴ × 3¹ × 5¹ = 16 × 3 × 5 = 240 \]

### Step 2: Calculate LCM of 12, 16, and 24 (Option B)
1. **Prime Factorization**:
- 12 = 2² × 3
- 16 = 2⁴
- 24 = 2³ × 3

2. **Identify the highest powers of each prime**:
- For 2: max(2², 2⁴, 2³) = 2⁴
- For 3: max(3¹) = 3¹

3. **Calculate LCM**:
\[ \text{LCM} = 2⁴ × 3¹ = 16 × 3 = 48 \]

### Step 3: Calculate LCM of 5, 18, and 20 (Option C)
1. **Prime Factorization**:
- 5 = 5¹
- 18 = 2 × 3²
- 20 = 2² × 5

2. **Identify the highest powers of each prime**:
- For 2: max(2¹, 2²) = 2²
- For 3: max(3²) = 3²
- For 5: max(5¹) = 5¹

3. **Calculate LCM**:
\[ \text{LCM} = 2² × 3² × 5¹ = 4 × 9 × 5 = 180 \]

### Step 4: Calculate LCM of 18, 24, and 56 (Option D)
1. **Prime Factorization**:
- 18 = 2 × 3²
- 24 = 2³ × 3
- 56 = 2³ × 7

2. **Identify the highest powers of each prime**:
- For 2: max(2¹, 2³) = 2³
- For 3: max(3², 3¹) = 3²
- For 7: max(7¹) = 7¹

3. **Calculate LCM**:
\[ \text{LCM} = 2³ × 3² × 7¹ = 8 × 9 × 7 = 504 \]

### Summary of Results
- A: 12, 80, 20 → LCM = 240
- B: 12, 16, 24 → LCM = 48
- C: 5, 18, 20 → LCM = 180
- D: 18, 24, 56 → LCM = 504

### Matching with List-II
- A matches with 240 (not listed)
- B matches with 48 (not listed)
- C matches with 180 (not listed)
- D matches with 504 (4)

### Final Answer
Based on the calculations, we can conclude:
- A → 240
- B → 48
- C → 180
- D → 504

### Codes:
- A: 3
- B: 1
- C: 2
- D: 4