00:01
So we have to find the smallest number that is a divisible by 105, 91, and 130.
00:08
So we really want to find the least common multiple.
00:12
And so this number is 5 times 21, and this is 3 times 7.
00:21
91 is, let's see, is that a prime? no, 7 goes into there, 13 times.
00:36
And then this is 13 times 10, which is 2 times 5.
00:42
So 105 is 5 times 3 times 7.
00:46
So we want to find the least common multiple, so we need to have a divisible by 2, and it has to have a factor of 3.
00:55
It has to have a factor of 5.
00:59
It has to have one factor of 7, and it has to have one factor of 13.
01:06
So this is 6 times 35 times 13.
01:13
So that would be 2 ,730 is the smallest number that is divisible by the three.
01:21
Next we have three bells, 15, 18, and 45 seconds respectively.
01:28
And we want to find how many seconds, will all three go together.
01:33
And so we know that this is 3 times 5.
01:37
We know that this is 9 times 2, so that is 2 times 3 squared.
01:43
And this is 9 times 5.
01:45
So this is 3 squared times 5.
01:48
So the least common multiple has to have a factor of 2.
01:53
It needs two factors of 3, and we need one factor of 5...