If X is a positive integer, what is the Least common multiple of X, 6, 9
1. the least common mulitple of x and 6 is 30
2. the least common multiple of x and 9 is 45
the OA is D but i got it to be C because I thought X could be either 5 or 15.
someone help?
gmat prep
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I actually got the same answer for the same reason. X could be either 5 or 15. Interesting!Mclaughlin wrote:If X is a positive integer, what is the Least common multiple of X, 6, 9
1. the least common mulitple of x and 6 is 30
2. the least common multiple of x and 9 is 45
the OA is D but i got it to be C because I thought X could be either 5 or 15.
someone help?
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I agree with D
Question is not about the value of x, it is about the LCM of three intergers
The key here is prime factorisation
rephrasing the main statement:
What is LCM of x, 2*3 (6=2*3), and 3^2 (9=3*3)
(1)
LCM of x and 2*3 is 30.
Factoring 30=2*3*5
this means that x has 5 as a factor. x can contain 2 and 3 but not necessary
answering the main question:
LCM of 2*3, 3^3 and x is 2*3^2*5=90
Let's check
x=5. LCM of 5, 6 and 9 is 90
x=10. LCM = 90
x=15. LCM = 90
SUFF
(2)
Using the same logic
LCM of x and 3^2 is 45
45 = 3^2*5
x has 5 as a factor
LCM of 5, 6 and 9 is 90
SUFF
Answer D
Remember,
that
LCM of 2 or more numbers is a product of all prime numbers, included into prime factorization at least one of these numbers, raised to the highest of two powers
GCD of 2 or more numbers is a product of prime numbers, included into prime factorization of all numbers, and raised to the smallest of two powers
Question is not about the value of x, it is about the LCM of three intergers
The key here is prime factorisation
rephrasing the main statement:
What is LCM of x, 2*3 (6=2*3), and 3^2 (9=3*3)
(1)
LCM of x and 2*3 is 30.
Factoring 30=2*3*5
this means that x has 5 as a factor. x can contain 2 and 3 but not necessary
answering the main question:
LCM of 2*3, 3^3 and x is 2*3^2*5=90
Let's check
x=5. LCM of 5, 6 and 9 is 90
x=10. LCM = 90
x=15. LCM = 90
SUFF
(2)
Using the same logic
LCM of x and 3^2 is 45
45 = 3^2*5
x has 5 as a factor
LCM of 5, 6 and 9 is 90
SUFF
Answer D
Remember,
that
LCM of 2 or more numbers is a product of all prime numbers, included into prime factorization at least one of these numbers, raised to the highest of two powers
GCD of 2 or more numbers is a product of prime numbers, included into prime factorization of all numbers, and raised to the smallest of two powers