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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?
(1) z is equal to the least common multiple of x, y and z.
(2) z is equal to 15 times the highest number that divides each of x, y and z completely.
(1) z is equal to the least common multiple of x, y and z.
(2) z is equal to 15 times the highest number that divides each of x, y and z completely.
04 Jun 2022, 04:51
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(1) z is equal to the least common multiple of x, y and z.
All this means is that x and y are both factors of z.
Eg. #1: \(x = 2\), \(y = 3\) & \(z = 30\). LCM = \(30\). Prime factors of 30: (\(3*5*2\))
Eg. #2: \(x = 2\), \(y = 3\) & \(z = 210\). LCM = \(210\). Prime factors of 210: (\(3*5*2*7\))
Both fit the info provided by the statement, however, we get two different answers.
INSUFFICIENT
(2) z is equal to 15 times the highest number that divides each of x, y and z completely.
As x and y are prime numbers, the only number that will divide x, y and z is 1. Which means that \(z = 15\)
Eg. #1: \(x = 2\), \(y = 3\) & \(z = 15\). LCM = \(30\). Prime factors of 30: (\(3*5*2\))
Eg. #2: \(x = 3\), \(y = 5\) & \(z = 15\). LCM = \(15\). Prime factors of 30: (\(3*5\))
Once again we get two different answers which immediately means that we do not have enough info to give a definite answer.
INSUFFICIENT
(1)+(2).
x and y are both factors of z, and \(z = 15\)
Factors of 15 that are prime numbers: \(3\)&\(5\).
Let \(x = 3\) & \(y =5\)
\(x = 3\), \(y = 5\) & \(z = 15\). LCM = \(15\). Prime factors of 15: (\(3*5\))
Answer is two prime factors.
SUFFICIENT
Answer C
All this means is that x and y are both factors of z.
Eg. #1: \(x = 2\), \(y = 3\) & \(z = 30\). LCM = \(30\). Prime factors of 30: (\(3*5*2\))
Eg. #2: \(x = 2\), \(y = 3\) & \(z = 210\). LCM = \(210\). Prime factors of 210: (\(3*5*2*7\))
Both fit the info provided by the statement, however, we get two different answers.
INSUFFICIENT
(2) z is equal to 15 times the highest number that divides each of x, y and z completely.
As x and y are prime numbers, the only number that will divide x, y and z is 1. Which means that \(z = 15\)
Eg. #1: \(x = 2\), \(y = 3\) & \(z = 15\). LCM = \(30\). Prime factors of 30: (\(3*5*2\))
Eg. #2: \(x = 3\), \(y = 5\) & \(z = 15\). LCM = \(15\). Prime factors of 30: (\(3*5\))
Once again we get two different answers which immediately means that we do not have enough info to give a definite answer.
INSUFFICIENT
(1)+(2).
x and y are both factors of z, and \(z = 15\)
Factors of 15 that are prime numbers: \(3\)&\(5\).
Let \(x = 3\) & \(y =5\)
\(x = 3\), \(y = 5\) & \(z = 15\). LCM = \(15\). Prime factors of 15: (\(3*5\))
Answer is two prime factors.
SUFFICIENT
Answer C
27 Sep 2023, 13:29
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