Graduate Management Admission Test (GMAT) Practice Test

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If number N must be a multiple of x and y, what is crucial to finding possible values?

Look for the greatest common factor of x and y
Look for their least common multiple
Identify the sum of x and y
Consider all prime factors of x and y

The correct answer is: Look for their least common multiple

To determine values of number N that must be a multiple of both x and y, finding their least common multiple (LCM) is crucial. The LCM of two numbers is the smallest positive integer that is divisible by both x and y. This means any multiple of the LCM will also be a multiple of both x and y. Understanding the least common multiple helps in identifying the smallest building block from which all required multiples can be generated. For example, if x is 4 and y is 6, their LCM is 12. Hence, any valid N must be one of the multiples of 12, such as 12, 24, 36, etc., ensuring that N will also be a multiple of both 4 and 6. Other approaches mentioned, like identifying the greatest common factor (GCF) or considering the sum of x and y, do not directly aid in determining multiples of both variables. Likewise, while analyzing prime factors can provide deeper insight into the numbers, it is not the most efficient or direct method to ascertain the multiples needed for N. Hence, focusing on the least common multiple is the most effective strategy in this scenario.