If A= { LCM of any two numbers <10} in tabular form
Answers
Answer:
I am finding a way show a simply way to do a LCM. Unfortunately a text editor is inadequate to do it. Alas, computer do wonders but writing a single envelope is a mess. Same for emulating a simple paper.
Basically, the way is to reduce every number to its prime numbers?
10 = 2 x 5
15 = 3 x 5
if a prime is common to both number, just use it once.
In this case, 2 x 5 x 3 x 5. Since 5 is common to 10 and 15, use it once.
2 x 3 x 5 = 30.
For other numbers, for example, 10, 15, 30, is a little more complicated:
10 = 2 x 5
15 = 3 x 5
30 = 2 x 3 x 5
Notice that 5 is common to all the numbers. Again, use it once. 2 is also common to two of the numbers. Use it once.
2 x 3 x 5 = 30
30 is the answer because it contains 10 three times, 15 is contained 2 times, 30 is contained once.
What about 10, 15, 45
10 = 2 x 5
15 = 3 x 5
45 = 3 x 3 x 5
Eliminating duplicates:
2 x 5 x 3 x 3 = 90.
Notice that 2 and 5 are contained in 10.
2 x 5
From the second number we take only 3 because 5 is already in the first and third.
2 x 5 x 3
Finally, from 45 we take only 3 because the first 3 is repeated in the second number. So, we add only the second 3. The 5 is left out because it is repeated in the first and second number.
2 x 5 x 3 x 3 = 90
This is simple but the explanation is weird.