Question

Find the smallest number when divided by 3,4,5,6 gives remainder 2,3,4,5 but exactly divisible by 7

Answer 1

☆☆ your answer is here☆☆

SOLUTION:--

Step 1- Find out the LCM of 2, 3, 4, 5, 6 which is 60.

Step 2- Add 1 to 60 which is 61.

Step 3- Multiple 61 by 7 repeatedly till it fulfills the condition that remainder should be 1.

Step 4- I got the answer 146461 which seems to correct.

So now my question is:

1) Is this answer correct? If yes how to verify that this is smallest number which fulfills above condition?

2) I think this is not the best way to do this question. So Can anyone give a better way to solve this problem?

Answer 2

The smallest number is 119.

Given,

The number is divided by 3,4,5,6 gives the remainder 2,3,4,5.

The number is exactly divisible by 7.

To Find,

The smallest number.

Solution,

Firstly, we have to find the LCM of 3,4,5,6.

So, let's understand the concept of LCM.

LCM stands for Least Common Multiple.

In mathematics, LCM refers to the process of finding the smallest common multiple between two or more numbers. Common multiples are numbers that are multiples of two or more numbers.

Now, let's take the LCM of 3,4,5,6.

The LCM of 3,4,5,6 is 60.

Let the smallest number be 'x.'

Now, we will find the Common Remainder.

2 3 4 5

3 4 5 6

1  1   1  1

The common remainder is 1.

Let the multiplying factor be y.

x = 60y -1

x = 56 y + 4y -1.

56 is divisible by 7 and 4y must be divisible by 7

So, we have to find the value of y

Let y = 2,

= 4 × 2 -1

= 7

7 is divisible by 7.

Now, we will put the value of y.

x = 60 × 2 -1

x = 120 -1

x = 119.

The smallest number is 119.

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