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Find the greatest 5 digit number that is exactly divisible by 22,25 and 30
Given :
Numbers 22,25 and 30
To find :
The greatest 5 digit number which is exactly divisible by 22,25 and 30
Solution :
If a number is divisible 22,25 and 30, then it must be a multiple for these numbers.
Let us find the smallest number which is divisible by 22,25 and 30. This is nothing but LCM of 22,25 and 30.
| LCM of 22, 25 and 30 | |||
|---|---|---|---|
| 2 | 22 | 25 | 30 |
| 5 | 11 | 25 | 15 |
| 3 | 11 | 5 | 3 |
| 11 | 11 | 5 | 1 |
| 5 | 1 | 5 | 1 |
| 1 | 1 | 1 | |
$2 \times 5 \times 3 \times 11 \times 5 = 1650$
So LCM is 1650.
The required number should be a multiple of 1650. It is also the smallest 5 digit number which is a multiple of 1650.
If we divide 10000 with 1650, we get a reminder of 100.
So 9900 is a multiple of 1650.
9900+ 1650 = 11550.
11550 is smallest 5 digit number which is multiple of 1650.
So, answer is 11550.
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