Question

What is the least number of apples a teacher should have so then when she distributes equal numbers of them to her 10,15 and 25 students ,no apples is left? Write in application of H. C. F and L. C. M

Answer 1

Correct Question -

What is the least number of apples a teacher should have so then when she distributes equal numbers of them to her 10, 15 and 25 students ,no apple is left?

Write in application of H. C. F and L. C. M .

Concept Used -

HCF and LCM

Solution -

In the above question , the following information is given -

When the teacher distributes the given number of apples among 10 students , no apples are left .

When the teacher distributes the given number of apples among 15 students , no apples are left .

When the teacher distributes the given number of apples among 25 students , no apples are left .

Now ,

Let us assume that the teacher has x apples .

Now,

When the teacher distributes the given number of apples among 10 students , no apples are left .

So, 10 is a factor of x.

When the teacher distributes the given number of apples among 15 students , no apples are left .

So, 15 is a factor of x.

When the teacher distributes the given number of apples among 25 students , no apples are left .

So, 25 is a factor of x.

Thus ,

10, 15 and 25 are three factors of x .

So ,

Least value of x

=> LCM of 10, 15 and 25

=>

5 |__10__15__25_

1 |__2___3____5_

Required LCM

=> 5 × 2 × 3 × 5

=> 10 × 15

=> 150 .

Thus , she needs to have a minimum of 150 apples to satisfy the given conditions .

________

Answer 2

$\huge\sf\pink{Answer}$

☞ The teacher should have 150 apples

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ There are 10,15,25 and students in a class

✭ Apples are distributed equally

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

☆ The least number of apples that the teacher should have?

$\rule{110}1$

$\huge\sf\purple{Steps}$

So here your answer can just be found just by finding the LCM of the three numbers

LCM(10,15,25)

➝ $\sf 10 = 2 × 5$

➝ $\sf 15 = 3 × 5$

➝ $\sf 25 = 5 × 5$

So taking the highest power of each factor,

$\sf\dashrightarrow{ LCM(10,15,25) = 2^1 × 3 ^ 1 × 5^2}$

$\sf\orange{\dashrightarrow LCM(10,15,25) = 150}$

$\rule{170}3$