The lcm of n,28 and 49 is 588. if n is an odd number, find all possible outcomes of n
Answers
Answer:
If n is odd number, so the possible value of n would be 3.
Answer:
The LCM of n, 28 and 49 is 588. If n is odd, find all the possible values of n.
n must be a factor of 588, find the prime factor of 588.
588: 2*588
2*294
3*147
7*49
7*7
Find the LCM of 28, 49
28: 2 squared, 7
49: , 7 squared
LCM: 2 squared, 7 squared
Therefore, 2 squared*7 squared*n = 588
588: 3
So if you take away 2 squared and 7 squared from 588's prime factors what is left will be 3. Hence, 3 is n.
3*2 squared*7 squared = 588
However, the question asked for all possible n that is an odd number.
Answer 2: find the common factors between 588,28,49
588 = 1*588 28 = 1*28 49 = 1*49
2*294 2*14 7*7
3*196 4*7
4*147
6*98
7*84
12*49
14*42
21*28
The common factor is 7. Remember that when we want to increase a numbers LCM, we need to multiply it by a prime number.
588*7 = 4116
4116's prime factors: 2
2
3
7
7
7
Take away 2 squared and 7 squared from 588's prime factors (28 and 49's prime factors):
4116's prime factors left: 3
7
3*7= 21
21 is one of the answer, since it is an odd number and it is a factor of 588.
Answer 3: Using the above method, 4116*7 =28812
28812's prime factors: 2
2
3
7
7
7
7
Take away 2 squared and 7 squared from 28812's prime factors (28 and 49's prime factors):
28812's prime factors left: 3
7
7
3*7*7 = 147
147 is one of the answer, since it is an odd number and it is a factor of 588.
In case you ware wondering why we can't go further and multiply 28812 by 7 and find more possible digits, it is because if you were to find the next digit, which is 3*7*7*7 = 1029, it is way larger than 588. Therefore, we can only find digits that is a factor of 588.
Answer: 3, 21 and 147.
Step-by-step explanation: