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?

Solution :

LCM of 8, 10, 14, 16 = 560
4 left out in each
Therefore 560 + 4
Which is perfectly divisible by 12 proving no students left when there is group of 12 students

Hence, the answer is 564 ​

Answer 1

Answer:

LCM of 8, 10, 14, 16 = 560

4 left out in each

Therefore 560 + 4

Which is perfectly divisible by 12 proving no students left when there is group of 12 students

Hence, the answer is 564

Answer 2

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

Given :-

• Students arranged in each row = 8, 10, 14 and 16 .
• Students left in each case = 4
• On arranging 12 students in each row no student is left .

To Find :- The least possible value of total number of students in yoga class ?

Concept used :-

• The least number which when divided by a, b and c leaves the same remainder ‘r’ each case = (LCM. of a, b and c) + r .

Solution :-

In order to find the least number of students in each row first we need to find the LCM of 8, 10, 14 and 16 .

So, prime factors of 8, 10, 14 and 16 are :-

→ 8 = 2 × 2 × 2

→ 10 = 2 × 5

→ 14 = 2 × 7

→ 16 = 2 × 2 × 2 × 2

then,

→ LCM = 2 × 2 × 2 × 2 × 5 × 7 = 560

therefore,

→ Remainder in each case = r = 4

→ Required least number of students = LCM(8, 10, 14, 16) + r = 560 + 4 = 564

now, when 12 students are arranged in each row,

→ Total students = 564

→ Students in each row = 12

then,

→ Total number of rows = 564 ÷ 12 = (47 × 12) ÷ 12 = 47 rows .

As we can see that, when 12 students are arranged in each row no student is left .

Hence, we can conclude that, the least possible value of total number of students in yoga class is equal to 564 students .

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