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# Find out the smallest number which when divided by any number from 2 to 10 the remainder will be 1.A. 2521B. 10000C. 5054D. 5500 Verified
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Hint: Type of question is based on the ‘lowest common factor’ which is abbreviated as LCM. According to the question we had to find out the smallest number which when divided by any of the numbers from 2 to 10(i.e. 2, 3, 4, 5, 6, 7, 8, 9, 10) then it will leave the remainder 1. In other words we have to find out the number which is divisible by all the numbers from 2 to 10 and always leave the remainder 1 when divided by these 2 to 10 numbers.

\begin{align} & 2=2 \\ & 3=3 \\ & 4=2\times 2 \\ & 5=5 \\ & 6=2\times 3 \\ & 7=7 \\ & 8=2\times 2\times 2 \\ & 9=3\times 3 \\ & 10=2\times 5 \\ \end{align}
$2\times 2\times 2\times 3\times 3\times 5\times 7=2520$
\begin{align} & =2520+1 \\ & =2521 \\ \end{align}