To get the multiples of 2:
= multiply 2 by 1, 2, 3, 4, 5, ...
2 x 1 = 2
2 x 2 = 4
2 x 3 = 6
2 x 4 = 8
2 x 5 = 10
Multiples of 2 are: 2, 4, 6, 8, 10, ...
Therefore the 3 multiples of 2 are : 2, 4, 6
3, 9, 15
They are the multiples of 6. Since there are infinitely many of them I will not even attempt to list all of them.
No. Such a list would be infinitely long.
lcm(2, 7) = 14 → first 3 common multiples are: 14, 28, 42; lcm(2, 8) = 8 → first 3 common multiples are: 8, 16, 24; lcm(7, 8) = 56 → first 3 common multiples are: 56, 112, 168; lcm(2, 7, 8) = 56 → first 3 common multiples are: 56, 112, 168.
Start counting from 2. For each number, if it has factors besides 1 and itself, then skip it; but if it doesn't have, then write it down. When you reach 10,000, you'll have the list, and you can count them. Here's another way to do it, which is probably easier: -- Write down all the numbers from 2 to 10,000. -- Start with 2. Cross all multiples of 2 off the list. -- Then go to 3. Cross all multiples of 3 off the list. -- 4 is gone ... it was a multiple of 2 ... so go on to 5. Cross all multiples of 5 off the list. -- 6 is gone ... it was a multiple of 2 and also of 3 ... so go on to 7. Cross all multiples of 7 off the list. -- 8, 9, and 10 are gone. Go on to 11. Cross all multiples of 11 off the list. -- Keep going like this, until you reach 5,000 . You'll have the list, and you can count them.
3, 9, 15
9, 18, 27.
They are the multiples of 6. Since there are infinitely many of them I will not even attempt to list all of them.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25} contains three multiples of 7.
3, 5, 6, 9, 12, etc are all multiples of 3 3, 7, 11, 34 are not multiples of any integer. Notice the first list contains numbers that can all be divided by the same number, 3. Thie second list the numbers cannot be divided by any number except 1.
No. Such a list would be infinitely long.
The one with multiples of 12.
No multiples of 2 are factors of 3.
lcm(2, 7) = 14 → first 3 common multiples are: 14, 28, 42; lcm(2, 8) = 8 → first 3 common multiples are: 8, 16, 24; lcm(7, 8) = 56 → first 3 common multiples are: 56, 112, 168; lcm(2, 7, 8) = 56 → first 3 common multiples are: 56, 112, 168.
Start counting from 2. For each number, if it has factors besides 1 and itself, then skip it; but if it doesn't have, then write it down. When you reach 10,000, you'll have the list, and you can count them. Here's another way to do it, which is probably easier: -- Write down all the numbers from 2 to 10,000. -- Start with 2. Cross all multiples of 2 off the list. -- Then go to 3. Cross all multiples of 3 off the list. -- 4 is gone ... it was a multiple of 2 ... so go on to 5. Cross all multiples of 5 off the list. -- 6 is gone ... it was a multiple of 2 and also of 3 ... so go on to 7. Cross all multiples of 7 off the list. -- 8, 9, and 10 are gone. Go on to 11. Cross all multiples of 11 off the list. -- Keep going like this, until you reach 5,000 . You'll have the list, and you can count them.
There are an infinite number of multiples of any number. Therefore, it is impossible to list all the multiples of 3 and 4. A list of the first 10 multiples: Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
There are infinitely many of them and so it is not possible to list them all.