# Case-1: Time and work

Example
Tatto can do a work in 10 days and Tappo can do the same work in 12 days. How many days will it take if both of them start working together?
Solution
Let us assume total work = LCM of (10, 12) units = 60 units. Now, since 60 units of work is being done by Tatto in 10 days, so Tatto is doing 6 units of work per day and similarly, Tappo is doing 5 units of work per day. Hence, together they are doing 11 units of work in one day. So, finally they will take  days to complete the work.

# Case-2: Time, speed and distance: Circular motion

Example
The speed of A is 15 m/s and the speed of B is 20 m/s. They are running around a circular track of length 1000 m in the same direction. After how much time will they meet at the starting point if they start running at same time?
Solution
Time taken by A in taking one round = 66.66
Time taken by B in taking one round = 50
LCM (66.66, 50) = 200

# Case-3: Number system: Tolling the bell

Example
There are two bells in a temple. Both the bells toll at a regular interval of 66.66 sec and 50 sec respectively. After how much time will they toll together for the first time?
Solution
Time taken by the 1st bell to toll = 66.66
Time taken by the 2nd bell to toll = 50
LCM (66.66, 50) = 200

It can be observed here that mathematical interpretation of both the questions are same, just the language has been changed.

# Case-4: Number system: Number of rows

Example
There are 24 peaches, 36 apricots and 60 bananas and they have to be arranged in several rows in such a way that every row contains the same number of fruits of one type. What is the minimum number of rows required for this to happen?
Solution
We can put one fruit in one row, and in (24 + 36 + 60) 120 rows, we can arrange all the fruits. Or, we can put two fruits in one row and can arrange all the fruits in 60 rows. But for the rows to be minimum, the number of fruits should be maximum in one row.

HCF of 24, 36, 60 = 12, so 12 fruits should be there in one row.

Hence, the number of rows = 10

# Case-5: Number system: Finding the remainder

Example
There is a number which when divided by 4 and 5 gives 3 as the remainder. What is the lowest three-digit number which satisfy this condition?
Solution
Let us assume that there is no remainder. So, the number has to be a multiple of LCM of 4 and 5. Now, LCM (4, 5) = 20
But there is a remainder of 3 when divided by 4 and 5. So, the number will be of the form (20N + 3).
Hence, the numbers are 23, 43, 63, 83, 103 and so onβ¦
So, 103 is the answer.