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Which of the following must be true...

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by BTGmoderatorLU » Tue Oct 24, 2017 1:55 pm
Which of the following must be true about two positive integers a and b

1)LCM of a and b can never be smaller than either a or b
2)The least possible value of GCD of a and b is 1
3)GCD of a and b can never be greater than either a or b

A)1,2,3
B)1 and 2
C)2 and 3
D)1 and 3
E)only 2

The OA is A.

Can any expert explain this PS question please? I don't have it clear. Thanks.
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by [email protected] » Wed Oct 25, 2017 7:22 pm
Hi LUANDATO,

We're told that A and B are positive integers. We're asked which of the following MUST be true (meaning 'which of the following is ALWAYS TRUE no matter how many different examples we can come up with?'). This question can be solved with a mix of Number Property rules and TESTing VALUES.

1)The Least Common Multiple of A and B can never be smaller than either A or B.

By definition, the LCM MUST of two numbers must be AT LEAST the value of the GREATER number.
For example:
The LCM of 1 and 4 is 4
The LCM of 2 and 3 is 6
The LCM of 3 and 5 is 15
Roman Numeral 1 IS true. Eliminate Answers C and E.

2) The least POSSIBLE value of the Greatest Common Divisor of A and B is 1.

We're asked to consider what the SMALLEST possibility of the GCD between two numbers COULD BE (under all possible circumstances). If one of the values is 1, then the GCD would be 1.
For example:
The GCD of 1 and 4 is 1
Roman Numeral 2 IS true. Eliminate Answer D.

3) The Greatest Common Divisor of A and B can never be greater than either A or B.

By definition, any divisor of a number will be equal to - or less than - that number. Thus, the largest that the GCD of 2 numbers can be is the value of the smaller number.
For example:
The GCD of 4 and 8 is 4
The GCD of 3 and 3 is 3
The GCD of 2 and 5 is 1
Roman Numeral 2 IS true. Eliminate Answer B.

Final Answer: A

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Rich
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