Question

find a remainder of 2 3 4 5 6 7 8 9 10 11 12 1 4 15 by 30?
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Answer 1

Answer:

Step-by-step explanation:

Before doing the actual problem, let's take the case of just 2 and 3 only. Just so I can make you visualise the solution, you are going to solve it, not me. I'll just guide you.

So, only 2 and 3 right? Gives off remainder 1 and 2. It's all about using information. So we know that the number's odd, and when divided by 3 gives remainder 2. The first number that satisfies this is 5. Go on, check it. The catch is the next number, which is 11 and the next, which is 17. Notice the fixed difference of 6. Keep that in mind for just a sec.

Now take the case for 2, 3 and 4. Using the above information we only need to search in the series 5, 11, 17,.. for numbers that give remainder 3 when divided by 4. Using trial and error, first number is 11. And the next number, that's 23. The difference? Fixed and equal to 12. Notice something?

Allow me to help. The thing to notice is the first number to satisfy is the LCM of the numbers - 1. And the next numbers can be obtained by adding the LCM to the previous value and so on.

So, if the LCM is x. Then the series is x-1, 2x-1, 3x-1 and so on.

Now the problem is easy, take the LCM of all the numbers, you only need the LCM of 5,7,8 and 9 (try to think why). This comes out to be 2520. Hence the first or lowest number that's the answer to your question is 2519. Better check it, I did the calculations in my head so I might be wrong.