Question

find the least number which when divided by 5 , 10 , 15 leave remainder 3 in each case​

Answer 1

Answer:

• The required number is 33.

Given:

When divided by 5,10 and 15 leaves remainder 3 in each case.

To Find:

• Find the least number

Solution:

5 = 5 × 1

10 = 2 × 5 × 1

15 = 3 × 5 × 1

LCM of 5,10 and 15 is = 5 × 2 × 3

LCM of (5,10 and 15) is = 30

Now we are given 3 as remainder left so now add it

Required number = LCM + Remainder = 30 + 3 = 33

As a result,33 is the smallest number,with a remainder of 3 in each case when divided by 5,10 and 15.

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Answer 2

Given :

• A number when when divided by 5 , 10 , 15 leave remainder 3 in each case.

To Find :

• The Least number

Concept :

• In this question, firstly we will find the LCM (Lowest Common Factor) of the given numbers, after that we will add the given remainder in the LCM.

Solution :

Taking LCM of 5 , 10 and 15 :

5 | 5 , 10 , 15

2 | 1 , 2 , 3

3 | 1 , 1 , 3

⠀ | 1 , 1 , 1

∴ LCM = 5 × 2 × 3 = 30

Now,

Adding the given remainder in LCM :

⇢ LCM + Given Reminder

⇢ 30 + 3

⇢ 33 ⠀⠀⠀⠀⠀[Required Number]

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Verification :

• In the Question itself is was given that the required number when divided by 5 , 10 , 15 leaves a remainder of 3.

In case of 5 :

• 33/5 = 5 × 6 = 30, so here we get a remainder of 3.

In case of 10 :

• 33/10 = 10 × 3 = 30, so here also we get a remainder of 3.

In case of 15 :

• 33/15 = 15 × 2 = 30, so here again we get a remainder of 3.

Hence it satisfy all the cases, So the Least number by which 5 , 10 and 15 should be divided to get a remainder of 3 is 33.

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