The LCM of two positive integers is twice the larger number.

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The LCM of two positive integers is twice the larger number. The difference of the smaller number and the GCD of the two numbers is 4. The smaller number is :

1. 12
2. 6
3. 8
4. 10

Correct Option: C

Let the numbers be x H and yH where H is the HCF and yH > x H.
∴ LCM = xy H
∴ xyH = 2yH ⇒ x = 2
Again, x H – H = 4
⇒ 2H – H = 4 ⇒ H = 4
∴ Smaller number = pH = 2 × 4 = 8