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vagabundo [1.1K]
3 years ago
12

Find the smallest 3-digit number which gives the remainder 1 when divided by 3 and by 4.

Mathematics
1 answer:
trasher [3.6K]3 years ago
4 0
Multiples of 3 plus 1 remainder are:

3n+1

Multiples of 4 plus 1 remainder are:

4n+1

Since these multiples must be the same number must be a multiple of 12 plus a remainder of one, which is:

12n+1

And the smallest such three digit number is:

12n+1>99  subtract 1 from both sides

12n>98  divide both sides by 12

n>8.17

Since n must be an integer, n=9

So then number is 12n+1

12(9)+1=109


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