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Match List -I with List -II and select t...

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):}`

Text Solution

AI Generated Solution

The correct Answer is:
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
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