The least common multiple of two numbers is 138. But their GCD is 23. The numbers are in the ratio 1 : 6. Which is the largest number among the two?

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Bihar STET TGT (Maths) Official Paper-I (Held On: 04 Sept, 2023 Shift 2)
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  1. 46
  2. 138
  3. 69
  4. 23

Answer (Detailed Solution Below)

Option 2 : 138
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Detailed Solution

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Explanation -

Let's denote the two numbers as x and 6x because they are in the ratio of 1:6.

We're given that the least common multiple (LCM) of x and 6x is 138 and their greatest common divisor (GCD) is 23.

We know that the product of two numbers equals the product of their GCD and LCM: 

Product of two number = GCD X LCM

x x 6x = 23 x 138

6x2 = 3174

x2 = 3174/6 = 529

x = 23

So, the smaller number x is 23, and the larger number 6x is 6 x 23 = 138. 

Therefore, the larger number among the two is 138.

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