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secondary 4 | E Maths
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Afternoon!!! Can someone help me with this question? i don’t understand it + the answer key :/
Thanks so much :)))
Date Posted: 4 years ago
Views: 257
Good afternoon Sonia! I just explained this exact question to one of my students yesterday.
Basically we need to find two numbers which have HCF of 15 and LCM of 450.
Now,
15 = 3 x 5
450 = 2 x 3 x 3 x 5 x 5 = 2 x 3^2 x 5^2
In other words, 15 contains one 3 and one 5, while 450 contains one 2, two 3s and two 5s.
The two numbers which we choose must meet the two conditions above.
If the two numbers contain exactly one 3 each, then the HCF condition is met, but the LCM condition is not met. This is because we take the higher of the power for the LCM if you recall.
Similarly, if the two numbers contain exactly two 3s each, then the LCM condition is met, but the HCF condition is not met. This is because we take the lower of the power for the HCF.
This means that one of the numbers must contain exactly one 3 and the other must contain exactly two 3s.
Similarly, one of the numbers must contain exactly one 5 and the other must contain exactly two 5s. And one of the numbers must contain exactly one 2 while the other does not contain any 2 at all.
There are many possible combinations of these.
For example, 2 x 3 x 5 and 3^2 x 5^2. Or 2 x 3 x 5^2 and 3^2 x 5. There are other combinations too, and all of these pairs meet the conditions above.
However, only one of these pairs of two numbers contain two numbers below 100, the pair of which is 2 x 3 x 5^2 and 3^2 x 5, or 90 and 75.
Let me know if you need more explanation and I will do my best to explain them again! I will write them later on paper if necessary to better illustrate my point and if no one else has written them yet.
Basically we need to find two numbers which have HCF of 15 and LCM of 450.
Now,
15 = 3 x 5
450 = 2 x 3 x 3 x 5 x 5 = 2 x 3^2 x 5^2
In other words, 15 contains one 3 and one 5, while 450 contains one 2, two 3s and two 5s.
The two numbers which we choose must meet the two conditions above.
If the two numbers contain exactly one 3 each, then the HCF condition is met, but the LCM condition is not met. This is because we take the higher of the power for the LCM if you recall.
Similarly, if the two numbers contain exactly two 3s each, then the LCM condition is met, but the HCF condition is not met. This is because we take the lower of the power for the HCF.
This means that one of the numbers must contain exactly one 3 and the other must contain exactly two 3s.
Similarly, one of the numbers must contain exactly one 5 and the other must contain exactly two 5s. And one of the numbers must contain exactly one 2 while the other does not contain any 2 at all.
There are many possible combinations of these.
For example, 2 x 3 x 5 and 3^2 x 5^2. Or 2 x 3 x 5^2 and 3^2 x 5. There are other combinations too, and all of these pairs meet the conditions above.
However, only one of these pairs of two numbers contain two numbers below 100, the pair of which is 2 x 3 x 5^2 and 3^2 x 5, or 90 and 75.
Let me know if you need more explanation and I will do my best to explain them again! I will write them later on paper if necessary to better illustrate my point and if no one else has written them yet.
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Good evening Sonia! Here are my written workings for this question. Let me know if you do not understand my workings and I will explain them again!
Date Posted:
4 years ago
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