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.
Find the least number which when divided by 16, 28, 40 and 77 leaves remainder 8 in each case. | |||
| Right Option : A | |||
| View Explanation | |||
Find the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively. | |||
| Right Option : C | |||
| View Explanation | |||
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 | |||
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