
Find the number nearest to “100000” and greater than “100000” which is exactly divisible by each of “8”,”15” and “21”?
A.100800
B.100600
C.110800
D.101800
Answer
491.4k+ views
Hint: To get the solution of such a question you need to find the lowest common factor of each all the given divisors, and once you get it then divide the given numbers with the obtained number to get the result. Lowest common factors are the values for the given numbers which can satisfy the condition of complete division of a number by the given set of numbers.
Complete step-by-step answer:
The number which has to be find should be greater than “100000”
Firstly finding the lowest common factor of the divisor “8”,”15”,”21” we get:
\[
\Rightarrow factors\,of\,8 = 1,2,4 \\
\Rightarrow factors\,of\,15 = 1,3,5 \\
\Rightarrow factors\,of\,21 = 1,3,7 \\
\Rightarrow lowest\,common\,factor\,of\,these\,numbers\,are = 1 \times 2 \times 4 \times 3 \times 5 \times 7 = 840 \;
\]
Here we found the lowest common factor, now on dividing each term we have to check for exact divisible, on solving we get:
\[
\Rightarrow the\,first\,given\,number\,is\,100800 \\
\Rightarrow on\,dividing\,with\,L.C.Mwe\,get\, \\
\Rightarrow \dfrac{{100800}}{{840}} = 120\,which\,is\,exact\,divisible \;
\]
Now when we check for other numbers, we do not get the exact divisible, so “100800” is our right answer.
So, the correct answer is “Option A”.
Note: The given number is very large to think for, but for small numbers you can directly check the divisibility by dividing the numbers separately by each term and get the solution.
For finding the lowest common factor you have to factorize the numbers and then get the common factors as individual factors, the common factors obtained will be count for one time and multiplied only one time with the rest of the factors obtained, the final product is our solution.
Complete step-by-step answer:
The number which has to be find should be greater than “100000”
Firstly finding the lowest common factor of the divisor “8”,”15”,”21” we get:
\[
\Rightarrow factors\,of\,8 = 1,2,4 \\
\Rightarrow factors\,of\,15 = 1,3,5 \\
\Rightarrow factors\,of\,21 = 1,3,7 \\
\Rightarrow lowest\,common\,factor\,of\,these\,numbers\,are = 1 \times 2 \times 4 \times 3 \times 5 \times 7 = 840 \;
\]
Here we found the lowest common factor, now on dividing each term we have to check for exact divisible, on solving we get:
\[
\Rightarrow the\,first\,given\,number\,is\,100800 \\
\Rightarrow on\,dividing\,with\,L.C.Mwe\,get\, \\
\Rightarrow \dfrac{{100800}}{{840}} = 120\,which\,is\,exact\,divisible \;
\]
Now when we check for other numbers, we do not get the exact divisible, so “100800” is our right answer.
So, the correct answer is “Option A”.
Note: The given number is very large to think for, but for small numbers you can directly check the divisibility by dividing the numbers separately by each term and get the solution.
For finding the lowest common factor you have to factorize the numbers and then get the common factors as individual factors, the common factors obtained will be count for one time and multiplied only one time with the rest of the factors obtained, the final product is our solution.
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Trending doubts
List some examples of Rabi and Kharif crops class 8 biology CBSE

How many ounces are in 500 mL class 8 maths CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

How many ten lakhs are in one crore-class-8-maths-CBSE

Name the states through which the Tropic of Cancer class 8 social science CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
