Discussion
If the LCM of two numbers is 138. But their GCD is 23. The numbers are in a ratio 1:6. Which is the largest number amongst the two?
Answer: B
With H.C.F. 23 the numbers are \( 23m \) and \( 23n \) with \( m \) and \( n \) coprime, and the ratio \( 1 : 6 \) makes them 23 and 138.
\[ \text{L.C.M.} = 23 \times 1 \times 6 = 138 \quad\checkmark \]
So the larger number is 138.
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