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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 and its Properties
The Least Common Multiple (LCM) of two numbers is the smallest multiple that is evenly divisible by both numbers. When analyzing the relationship between two numbers, x and y, where y is a multiple of x, we can derive the LCM effectively.
Defining the Relationship
- Let x be a number.
- Let y be a multiple of x, which can be expressed as y = kx, where k is an integer.
Finding the LCM
To find the LCM of x and y:
1. Identify the multiples:
- The multiples of x are x, 2x, 3x, ...
- The multiples of y (k*x) are y, 2y, 3y, ...
2. Common multiples:
- Since y is already a multiple of x, all multiples of y will also be multiples of x.
3. Smallest Multiple:
- The smallest multiple that includes both x and y is simply y (since y = kx).
Conclusion
Thus, the LCM of x and y, where y is a multiple of x, is given by:
- Correct Answer: y
This is option 'B', which confirms that when y is a multiple of x, the LCM is indeed y itself. This property simplifies the calculation of LCM for cases where one number is directly a multiple of another.
Community Answer
LCM of the given number ‘x’ and ‘y’ where y is...
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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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