Question

find the smallest number which when divided by 3,5,7 and 9 leaves remainder 1, 3, 5 and 7 respectively

Answer 1

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Answer 2

Answer: Our smallest number will be 313.

Step-by-step explanation:

We need to find the smallest number which when divided by 3,5,7,9 leaves remainder 1,3,5,7 respectively.

First we take the L.C.M of 3,5,7,9.

L.C.M of 3,5,7,9 is given by

$3\times 3\times 5\times 7\\\\=315$

And in each case 1,3,5 and 7 respectively.

i.e.

$3-1=2\\\\5-3=2\\\\7-5=2\\\\9-7=2$

Therefore, in each case 2 is the remainder.

So, our smallest number will be 315-2=313