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LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by
  • a)
    x
  • b)
    y
  • c)
    xy
  • d)
    x/y
Correct answer is option 'B'. Can you explain this answer?
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LCM of the given number ‘x’ and ‘y’ where y is...
Understanding LCM
The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both. In this case, we are examining the LCM of two numbers, 'x' and 'y', where 'y' is a multiple of 'x'.
Relationship between 'x' and 'y'
- Given that 'y' is a multiple of 'x', we can express this as:
- y = k * x (where k is a positive integer)
Finding the LCM
To find the LCM of 'x' and 'y':
- Since 'y' can be expressed as a multiple of 'x', the LCM will also be based on 'x'.
- The LCM will be the larger of the two numbers since 'y' is already a multiple of 'x'.
Mathematical Derivation
- LCM(x, y) can be simplified:
- LCM(x, y) = LCM(x, kx) = kx (which is 'y')
Thus, since 'y' is a multiple of 'x', the LCM simplifies to 'y'.
Conclusion
- The correct answer is option 'B' (y), because when one number is a multiple of another, the LCM is simply the larger multiple, which in this case is 'y'.
This reasoning confirms that understanding the relationship between the two numbers is crucial in determining their LCM effectively.
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LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given bya)xb)yc)xyd)x/yCorrect answer is option 'B'. Can you explain this answer?
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