If the HCF and LCM of two consecutive (positive) even numbers

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If the HCF and LCM of two consecutive (positive) even numbers be 2 and 84 respectively, then the sum of the numbers is

1. 30
2. 26
3. 14
4. 34

Correct Option: B

Let the numbers be 2p and 2q , where p and q are prime to each other.
∴ LCM = 2pq
⇒ 2pq = 84
⇒ pq = 42 = 6 × 7
Here p = 6 and q = 7
∴ Numbers are 2p = 2 × 6 = 12 and 2q = 2 × 7 = 14.
Hence , Sum of numbers = 12 + 14 = 26