What is the LCM of the numbers 3, a, and 7, if ‘a’ is an integer and a

Question

What is the LCM of the numbers 3, a, and 7, if ‘a’ is an integer and a ≥ 3?

Statement 1. ‘a’ is a prime number greater than 2.
Statement 2. Both GCD (3, a) and LCM (3, a) are factors of the number 30.

prateekjaiswal0911 · Answer

Statement 2 is sufficient. Answer Choice B.

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chetan2u · Answer

What is the LCM of the numbers 3, a, and 7, if ‘a’ is an integer and a ≥ 3?

Statement 1. ‘a’ is a prime number greater than 2.
a could be 3,5,7... LCM will be different in each case..
Insufficient
Statement 2. Both GCD (3, a) and LCM (3, a) are factors of the number 30.
a can be 3.. both GCD and LCM are 3
a can be 5.. GCD is 1 and LCM is 15, again both factors of 30
Insufficient

Combined..
a can still be 3 or 5
Insufficient

E

tanas · Answer

Statement 1 Doesn't help in finding the LCM as a could be either 3 or any other prime. If it is 3 then the LCM is 21 else it is '21a'

Statement 2 By itself is also not sufficient as a could be both 3 or 5. If a is 3 then the LCM of a and 3 is 3 which is a factor of 30, and the GCD is also 3. If a is 5 then LCM is 15 again a factor of 30, and its GCD is 1 which is also a factor.

Both statements together will also not help us to get to the value of a which could be either 3 or 5.

Hence the answer is that both statements taken together are not sufficient.

EgmatQuantExpert · Answer

Solution

Given:  
 • a is an integer
• a ≥ 3

To find:  
 • The LCM of (3, a, 7)

Analysing Statement 1  
 • As per the information given in statement 1, ‘a’ is a prime number greater than 2
 o Therefore, ‘a’ can have values like 3, 5, 7, 11 etc

• If a = 3, LCM (3, a, 7) = LCM (3, 3, 7) = 21
• If a = 5, LCM (3, a, 7) = LCM (3, 5, 7) = 105
• If a = 7, LCM (3, a, 7) = LCM (3, 7, 7) = 21

We can see, for different values of a, we are getting different LCM values

Hence, statement 1 is not sufficient to answer

Analysing Statement 2  
 • As per the information given in statement 2, both GCD (3, a) and LCM (3, a) are factors of the number 30
 o Factors of 30 = 1, 2, 3, 5, 6, 10, 15, and 30 
• If a = 3, GCD (3, a) = GCD (3, 3) = 3 and LCM (3, 3) = 3
 o 3 is a factor of 30 
• If a = 5, GCD (3, a) = GCD (3, 5) = 1 and LCM (3, 5) = 15
 o Both 1 and 15 are factors of 30

We can see a can have multiple possible values which satisfy the given statement

Hence, statement 2 is not sufficient to answer

Combining Both Statements  
Even after combining the statements, we can say 
 • a can be 3 or 5 – hence unique value of a cannot be determined

Hence, the correct answer is option E.

Answer: E

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What is the LCM of the numbers 3, a, and 7, if ‘a’ is an integer and a

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