GMAT Question > If the product of two positive integers is 54...

If the product of two positive integers is 540, which of the following can be the least common multiple and the greatest

common divisor respectively of the two integers?

I. 108 and 5

II. 90 and 6

III. 27 and 20

common divisor respectively of the two integers?

I. 108 and 5

II. 90 and 6

III. 27 and 20

- a)I only
- b)II only
- c)III only
- d)I, II and III
- e)None of the above

Correct answer is option 'B'. Can you explain this answer?

- Let the 2 positive integers be A and B
- A*B = 540

- To answer the question, we’ll evaluate the constraints on LCM(A,B) and GCD(A,B):
- Constraint 1: LCM(A,B) * GCD(A,B) = A*B
- Constraint 2: The LCM(A,B) contains the highest power EACH prime factor of A and B.
- This means, every prime factor that occurs in either one or both of A and B is represented in the LCM(A,B)
- So, every prime factor that occurs in the product of A and B will also occur in LCM(A,B)

- This means, every prime factor that occurs in either one or both of A and B is represented in the LCM(A,B)

- Next, we’ll find which of the 3 pairs satisfy both the above constraints

**Evaluating the 2 constraints****Constraint**1: LCM(A,B) * GCD(A,B) = 540**Constraint**2:- 540 = 2
^{2}*3^{3}*5- The prime factors of 540 are 2, 3 and 5

- So, the prime factors of LCM(A,B) are 2, 3 and 5

- 540 = 2

- Checking the 3 pairs
- 108 and 5
- The product of 108 and 5 is 540. So, the first Constraint is satisfied
- 108 = 2 *3
- The prime factors of 108 are not 2, 3 and 5. So, Constraint 2 is not satisfied
- So, this pair is rejected

- 108 and 5

- 90 and 6
- The product of 90 and 6 is 540. So, the first Constraint is satisfied
- 90 = 2*3 *5
- The prime factors of 90 are 2, 3 and 5. So, Constraint 2 is also satisfied

- So, this pair is possible

- 27 and 20
- The product of 27 and 20 is 540. So, the first Constraint is satisfied
- 27 = 3
^{3}- The prime factors of 27 are not 2, 3 and 5. So, Constraint 2 is not satisfied

- So, this pair is rejected

Looking at the answer choices, we see that the correct answer is **Option B**

View courses related to this question | Explore GMAT courses |

Explore GMAT courses View courses related to this question |

1 Crore+ students have signed up on EduRev. Have you? |

Question Description

If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for GMAT 2023 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.

If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for GMAT 2023 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.

Solutions for If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the product of two positive integers is 540, which of the following can be the least common multiple and the greatestcommon divisor respectively of the two integers?I. 108 and 5II. 90 and 6III. 27 and 20a)I onlyb)II onlyc)III onlyd)I, II and IIIe)None of the aboveCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.

Given: Let the 2 positive integers be A and B A*B = 540To Find:Which of the 3 pairs of numbers can be LCM(A,B) and GCD(A,B) respectivelyApproach: To answer the question, well evaluate the constraints on LCM(A,B) and GCD(A,B): Constraint 1: LCM(A,B) * GCD(A,B) = A*B Constraint 2: The LCM(A,B) contains the highest power EACH prime factor of A and B. This means, every prime factor that occurs in either one or both of A and B is represented in the LCM(A,B) So, every prime factor that occurs in the product of A and B will also occur in LCM(A,B) Next, well find which of the 3 pairs satisfy both the above constraintsWorking out: Evaluating the 2 constraints Constraint 1: LCM(A,B) * GCD(A,B) = 540 Constraint 2: 540 = 22 *33 *5 The prime factors of 540 are 2, 3 and 5 So, the prime factors of LCM(A,B) are 2, 3 and 5 Checking the 3 pairs 108 and 5 The product of 108 and 5 is 540. So, the first Constraint is satisfied 108 = 2 *3 The prime factors of 108 are not 2, 3 and 5. So, Constraint 2 is not satisfied So, this pair is rejected 90 and 6 The product of 90 and 6 is 540. So, the first Constraint is satisfied 90 = 2*3 *5 The prime factors of 90 are 2, 3 and 5. So, Constraint 2 is also satisfied So, this pair is possible 27 and 20 The product of 27 and 20 is 540. So, the first Constraint is satisfied 27 = 33 The prime factors of 27 are not 2, 3 and 5. So, Constraint 2 is not satisfied So, this pair is rejectedLooking at the answer choices, we see that the correct answer is Option B