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28 Nov 2016, 11:38
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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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
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
28 Nov 2016, 12:37
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stonecold
Which of the following must be true about positive integers a and b
1) The 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) The 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
1) The 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) The 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
Nice question!
1) The LCM of a and b can never be smaller than either a or b
The least common multiple (LCD) is a MULTIPLE of both a and b. So, the LCD must be greater than or equal to both a and b.
In other words, the LCM of a and b can never be smaller than either a or b
TRUE!
(this allows us to eliminate answer choices C and E)
2) The least possible value of the GCD (greatest common divisor) of a and b is 1
1 is a factor (divisor) of all positive integers.
Since the GCD of two positive integers is always greater than or equal to 1, the least possible value of the GCD (greatest common divisor) of a and b is 1
For example, of a = 2 and b = 3, the GCD of a and b is 1
TRUE!
(this allows us to eliminate answer choice D)
3) The GCD (greatest common divisor) of a and b can never be greater than either a or b
Since the divisors of an integer are always less than or equal to that integer, we can be certain that the GCD of a and b cannot be greater than either a or b
TRUE!
Answer:
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02 Nov 2019, 11:25
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