Statement Sums Involving L.C.M.
Statement Sums Involving L.C.M.
These are the following methods , used to solve the statement problems of LCM :
1.The product of the two numbers is always equal to the product of their HCF and LCM.
2. In LCM, if a single remainder is given, then firstly the LCM is calculated and then that single reminder is added in that.
3. In LCM, if for different numbers different remainders are given, then the difference between the number and its respective remainder will be equal. In that case, firstly the LCM is calculated, then that common difference between the number and its respective remainder is subtracted from that.
4. Whenever the question talks about the smallest or minimum, then in most of the cases it will be a question of LCM.
Secondly, whenever the word ‘together’ or ‘simultaneous’ is used in the question, then in all the cases it is LCM.
Illustration 1: Find the least number which when divided by 8, 12, 20 and 36 leaves remainders 6, 10, 18 and 34 respectively.
Solution : Factors of 8 = 2 2
2 , Factors of 12 = 2
2
3 , Factors of 20 = 2
2
5 and Factors of 36 = 2
2
3
3
The LCM of 8, 12, 20, and 36 is 360.
The difference between numbers and the respective remainders is equal to 2. we will subtract 2 to the LCM. So, the number is 360 - 2 = 358.
Illustration 2 : Find the least number which when divided by 6, 14, 18 and 22 leaves remainder 4 in each case.
Solution : Factors of 6 = 2 3 , Factors of 14 = 2
7 , factors of 18 = 2
3
3 and factors of 22 = 2
11
The LCM of 6, 14, 18 and 22 is 1386.
In order to get remainder 4 in each case, we will add 4 to the LCM. So, the number is 1386 + 4 = 1390.
There are 56 students in section A and 58 students in section B of a class in a school. Find the minimum number of books required for their class library so that they can be distributed equally among the students of section A or section B. | |||
| Right Option : B | |||
| View Explanation | |||
Find the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively. | |||
| Right Option : C | |||
| View Explanation | |||
Find the least number which when divided by 16, 28, 40 and 77 leaves remainder 8 in each case. | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [10]
My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thIt was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
