If a and b are Two Positive Integers and their LCM is c GMAT Problem Solving

Question: If a and b are two positive integers and their LCM is c. Which of the following cannot be the value of c?

1. a
2. b
3. a/b
4. a×b
5. a-b

Correct Answer: E
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• a and b are two positive integers
• LCM of a and b is c.

Find out:

• Which cannot be the value of c?

Hence we have two positive integers a and b, and their LCM is c.

Case 1: Let, a = 2, and b = 1
The LCM of a, b = LCM of 2,1 = 2
This satisfies the first option that the LCM is c. Thus c can be equal to a.

Case 2: Let a= 1, and b = 2
The LCM of a, b = LCM of 1,2 = 2
This satisfies the second option that the LCM is c. Thus c can be equal to b.

Case 3: Let a= 3 and b = 1
The LCM of a, b = LCM of 3,1 = 3
Also, a/b = 3/1= 3
This satisfies the third option that the LCM is c. Thus c can be equal to a/b.

Case 4: Let a = 2, and b= 3
The LCM of a, b = LCM of 2,3 = 6
Also, a*b = 2*3= 6
This satisfies the fourth option that the LCM is c. Thus c can be equal to a*b.

Case 5: Let a= 4 and b = 2
The LCM of a, b = LCM of 4,2 = 4
Here, a-b = 4-2 = 2, which is not equal to the LCM c.
Therefore, the fifth option that LCM c equals a-b doesn't hold true for the given statement. Hence, option E cannot be the value of LCM c.

Approach Solution 2:

Given that a and b are two positive integers and their LCM is c.
The question asks to find out which cannot be the value of c.

Let's analyse each of the options:

1. a

For example, LCM of 1, 5 = 5 –> 5 is one of the integers.
Hence option A gets eliminated.

2. b

For example, LCM of 1, 7 = 7 –> 7 is one of the integers.
Hence option B gets eliminated.

100. a/b

For example, LCM of 10,1 = 10 ---> 10/1 = 10
Hence option C gets eliminated

500. a×b

For example, LCM of 3,5 = 15 ---> 3*5 = 15
Hence option D gets eliminated

5. a-b

For example, LCM of 4,2 = 4 --> 4 - 2 = 2 ≠ 4
Hence, option E is the right answer since it cannot be the value of c.

Approach Solution 3:

The problem statement informs that:

Given:

• a and b are two positive integers
• LCM of a and b is c.

Find out:

• Which cannot be the value of c?

Let's assume the value of a and b to find the answer.

1. a

Let, a = 6, and b = 2
The LCM of a, b = LCM of 6,2 = 6
This satisfies the first option that the LCM c can be equal to a.

2. b

Let a= 2, and b = 6
The LCM of a, b = LCM of 2,6 = 6
This satisfies the second option that the LCM c can be equal to b.

100. a/b

Let a= 5 and b = 1
The LCM of a, b = LCM of 5,1 = 5
Also, a/b = 5/1= 1
This satisfies the third option that the LCM c can be equal to a/b.

500. a x b

Let a = 3, and b= 7
The LCM of a, b = LCM of 3,7 = 21
Also, a*b = 3*7= 21
This satisfies the fourth option that the LCM c can be equal to a*b.

5. a – b

Let a= 3 and b = 2
The LCM of a, b = LCM of 3,2 = 6
Here, a-b = 3 – 2 = 2, which is obviously not equal to the LCM c.
Therefore, the fifth option is the right answer.

“If a and b are two positive integers and their LCM is c”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This book has been taken from the book “GMAT Advanced Quant”. To solve the GMAT Problem Solving questions, the candidates must have a concrete knowledge of mathematics. The candidates can follow GMAT Quant practice papers to practice different types of questions that will enable them to improve their mathematical skills.

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