
Find out the smallest number which when divided by any number from 2 to 10 the remainder will be 1.
A. 2521
B. 10000
C. 5054
D. 5500
Answer
409.8k+ views
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.
Complete step by step answer:
As concept says we will simply find the LCM of these numbers and add the value which we want as a remainder then we will get the lowest number which when divided by some given numbers then we will get the required remainder. So according to the given condition we will first find the LCM of numbers from 2 to 10 and add 1 to it as we want it as a remainder. So we will get the answer.
So we will get the answer by concept, we will find LCM of 2, 3, 4, 5, 6, 7, 8, 9, 10.
Factors of numbers are;
$\begin{align}
& 2=2 \\
& 3=3 \\
& 4=2\times 2 \\
& 5=5 \\
& 6=2\times 3 \\
& 7=7 \\
& 8=2\times 2\times 2 \\
& 9=3\times 3 \\
& 10=2\times 5 \\
\end{align}$
So LCM of these numbers is;
$2\times 2\times 2\times 3\times 3\times 5\times 7=2520$
So 2520 is the LCM of numbers from 2 to 10. Now to get the value which always leaves a remainder 1 after division, so add 1 in 2520 so get the final answer. So we will get
$\begin{align}
& =2520+1 \\
& =2521 \\
\end{align}$
So, the correct answer is “Option A”.
Note: While solving the value we get on finding the LCM of numbers from 2 to 10 i.e. 2520 will give the remainder zero when divided by any of the numbers ranging from 2 to 10.
Complete step by step answer:
As concept says we will simply find the LCM of these numbers and add the value which we want as a remainder then we will get the lowest number which when divided by some given numbers then we will get the required remainder. So according to the given condition we will first find the LCM of numbers from 2 to 10 and add 1 to it as we want it as a remainder. So we will get the answer.
So we will get the answer by concept, we will find LCM of 2, 3, 4, 5, 6, 7, 8, 9, 10.
Factors of numbers are;
$\begin{align}
& 2=2 \\
& 3=3 \\
& 4=2\times 2 \\
& 5=5 \\
& 6=2\times 3 \\
& 7=7 \\
& 8=2\times 2\times 2 \\
& 9=3\times 3 \\
& 10=2\times 5 \\
\end{align}$
So LCM of these numbers is;
$2\times 2\times 2\times 3\times 3\times 5\times 7=2520$
So 2520 is the LCM of numbers from 2 to 10. Now to get the value which always leaves a remainder 1 after division, so add 1 in 2520 so get the final answer. So we will get
$\begin{align}
& =2520+1 \\
& =2521 \\
\end{align}$
So, the correct answer is “Option A”.
Note: While solving the value we get on finding the LCM of numbers from 2 to 10 i.e. 2520 will give the remainder zero when divided by any of the numbers ranging from 2 to 10.
Recently Updated Pages
Questions & Answers - Ask your doubts

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Science: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

Difference Between Plant Cell and Animal Cell

What is pollution? How many types of pollution? Define it

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Distinguish between Conventional and nonconventional class 9 social science CBSE
