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kiran120680
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23 Mar 2019, 23:00
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If x, y and z are distinct positive integers where x and y are prime numbers, find the number of prime factors of the lowest number that has x, y and z as its factors?
I. z is equal to the least common multiple of x, y and z.
II. z is equal to 15 times the highest number that divides each of x, y and z completely.
I. z is equal to the least common multiple of x, y and z.
II. z is equal to 15 times the highest number that divides each of x, y and z completely.
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24 Mar 2019, 07:54
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If x, y and z are distinct positive integers where x and y are prime numbers, find the number of prime factors of the lowest number that has x, y and z as its factors?
We are looking for the LCM of x, y and z.
I. z is equal to the least common multiple of x, y and z.
This tells us that x and y are factors of z as x and y are prime numbers.
But we do not know any value of variables
Insuff
II. z is equal to 15 times the highest number that divides each of x, y and z completely.
Since x and y are prime numbers, their greatest divisor would be 1, so z is 15 times 1 or 15*1=15.
But we do not know anything about 15..
say x=2, y =7, and z is 15, the answer is 210, but say x =3 and y =5, and z is 15, the answer is 15.
Insuff
Combined.
x and y are prime factors of z, and z is LCM of z, x and y. z is 15, thus answer is 15.
Suff
We are looking for the LCM of x, y and z.
I. z is equal to the least common multiple of x, y and z.
This tells us that x and y are factors of z as x and y are prime numbers.
But we do not know any value of variables
Insuff
II. z is equal to 15 times the highest number that divides each of x, y and z completely.
Since x and y are prime numbers, their greatest divisor would be 1, so z is 15 times 1 or 15*1=15.
But we do not know anything about 15..
say x=2, y =7, and z is 15, the answer is 210, but say x =3 and y =5, and z is 15, the answer is 15.
Insuff
Combined.
x and y are prime factors of z, and z is LCM of z, x and y. z is 15, thus answer is 15.
Suff
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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