Question

A Yoga instructor wants to arrange students in rows with equal number of students in each row. If he arranges
8.10.14 or 16 students in each row, then four students are left in each case. On arranging 12 students in each
row no student is left. What is the least possible value of total number of students in yoga class?​

Answer 1

Step-by-step explanation:

Take LCM of 8,10,14 ,16

it will give you Total students in row....then add 16

gives you Total students

Answer 2

Given:

No. of students left out = 4

No. of students in each row = 12

To find:

The total no. of students in yoga class.

Solution:

When the yoga instructor arranges the students in $8,10,14$ or $16$ students in a row, there will always be $4$ students left out. On determining the LCM of $8,10,14,16$ we can get a possible value for the total no. of students. Determine the factors of each number and then find the LCM of these numbers.

$8=2*2*2$

$10=2*5$

$14=2*7$

$16=2*2*2*2$

Here, the LCM = $2*2*2*2*5*7=560$

When arranging these $560$ students in $8,10,14$ or $16$ per row, there will always be $4$ students remaining. Add these $4$ students to $560$ students to get $564$ students. Now, $564$ is divisible by $12$. On arranging $12$ students in each row, no student is left out. So, the total number of students attending the yoga class is $564$.

The least possible value of total number of students in yoga class is 564.