What is the smallest whole number which is exactly divisible by 1 -10 inclusive?

Answer 1

11

Answer 2

The answer to the question is 2520. It may seem complicated at first, but when you start to understand how to do it, you won't even have to think about all the trouble! Let me elaborate on the answer a bit:

You need a number that is divisible by the numbers 1 through 10, so, you want to find all the factors of the above numbers:

1 = 1

2 = 1*2

3 = 1*3

4 = 1*2*2

5 = 1*5

6 = 1*2*3

7 = 1*7

8 = 1*2*2*2

9 = 1*3*3

10 = 1*2*5

So, looking at the above, the smallest whole number that you want will have the factors: 1*2*5*3*3*2*2*7 which when multiplied together is 2520.

How did I pick those numbers? Least common multiple. start by pulling out 1 copy of each Prime number up to 10: take away a 1, 2, 3, 5, and 7 multiple and you are left with:

4 has a 2 remaining

8 has a 2*2 remaining

9 has a 3 remaining

now take away another 2 multiple:

8 has a 2 remaining

9 has a 3 remaining

now take away another 2 multiple:

9 has a 3 remaining

now take away another 3 multiple, and you have your factors needed: 1, 2, 3, 5, 7, 2, 2, 3, which when multiplied together gives you the smallest whole number evenly divisible by the whole numbers 1-10, which is 2520.

A faster way is to look for all of your prime numbers that are factors, and whenever you find a power of such you just take that highest power, so:

1, 2^3, 3^2, 5, 7

and then multiply all of those together, which is: 1*8*9*5*7