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Thủ Thuật về Find the smallest number which when divided by 6,8 and 12 leaves same remainder 2 in each case 2022

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What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case remainder 2 but when divided by 13 leaves no remainderA.312B.962C.1562D.1586

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    What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case remainder 2 but when divided by 13 leaves no remainderA.312B.962C.1562D.1586 Answer: 95 is the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case.Hence, 95 is the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case.What is the least number which when divided by 6 7 8 and 9 will give a remainder of 3 in each case?What is the smallest number which when divided by 7 8 9 leaves a remainder of 2 4 6?What will be the smallest number which when divided by 6 7 8 9 and 12 leaves remainder 2
    Each time?What is the least number which when divided by 5 6 7 and 8 leaves a remainder 3 but when divided by 9 leaves no remainder *?What is the smallest number which has 6 8 and 12 as factor?What is the least number that when divided by 6 9 and 12 leaves a remainder of 5?What is the smallest number that can be divided by 6 9 and 12 without a remainder?What will be the smallest number which when divided by 6 7 8 9 and 12 leaves remainder 2 Each time?
    What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case remainder 2 but when divided by 13 leaves no remainderA.312B.962C.1562D.1586
    Answer: 95 is the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case.Hence, 95 is the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case.What is the least number which when divided by 6 7 8 and 9 will give a remainder of 3 in each case?What is the smallest number which when divided by 7 8 9 leaves a remainder of 2 4 6?What will be the smallest number which when divided by 6 7 8 9 and 12 leaves remainder 2 Each time?What is the least number which when divided by 5 6 7 and 8 leaves a remainder 3 but when divided by 9 leaves no remainder *?

Answer

Verified

Hint: Hint- To find the least number we have to
calculate the the LCM of the given numbers first then we will set the number as 120k+2 as in the question given that remainder is 2. Then check for what value of k the number is divisible by 13. At last put the value of k and find the required least number.

Complete step-by-step answer:
Complete step by step solution:
The given numbers are 3, 5, 6, 8, 10 and 12
Take LCM of them we get,
 $ Rightarrow $ LCM of 3, 5, 6, 8, 10 and 12 [ = 2 times 2 times 2 times 3
times 5 = 120]
As question says that the least number leaves remainder 2 when divided by the numbers 3, 5, 6, 8, 10 and 12
So the required number we can write as
∴Required number [ = left( 120k + 2 right)]
Question also says that the required number is also divisible by the 13
So it can be possible when the value of k is equal to 8
(120k+2) is divisible by 13 then k =8
On putting the value of k in the (120k+2)
We get,
 $ Rightarrow $ Required number [
= 120 times 8 + 2 = 962]
Hence the least number which leaves remainder 2 when divided by 3, 5, 6, 8, 10 and 12 is 962.
So, the correct answer is “Option B”.

Note: Question asked that the least number there can be more than one number that can be divisible by numbers 3, 5, 6, 8, 10 and 12 and leaves the remainder 2. So students should be aware of that.

Given:

The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3

The
least number when divided by 9 remainder = 0

Concept Used:

For the least number take LCM and also check that all conditions are satisfying or not

For same remainder in each case add the remainder in the LCM 

Calculation:

First we have to find the LCM of 5, 6, 7, 8

5 = 51

6 = 21 × 31 

7 = 71 

8 = 23 

LCM of 5, 6, 7, 8 is 23 × 31 × 51 × 71 = 840

For
same remainder we have to add 3 to the LCM

⇒ 840 + 3 

Now check weather it is divisible by 9 or not

843/9 = Not divisible by 9

Now we have to take next multiple of LCM and then add 3

840 × 2 + 3

⇒ 1683

Divide it by 9

1683/9 = 187

⇒ 1683 is divisible by 9 

⇒ 1683 is the least number when divided by 5, 6, 7, 8 gives remainder 3

Shortcut Trick

The least number must be divisible by 9 

For divisibility of 9 sum of digits of the number must be divisible by 9 

Checking it by options:

Option 1) 1677

1 + 6 + 7 + 7 = 21

⇒ 1677 is not divisible by 9

Option
2) 1683

1 + 6 + 8 + 3 = 18

⇒ 1683 is divisible by 9

Option 3) 2523

2 + 5 + 2 + 3 = 12

⇒ 2523 is not divisible by 9

Option 4) 3363

3 + 3 + 6 + 3 = 15

⇒ 3363 is not divisible by 9

∴ The least number is 1683 which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.

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LCM is the smallest positive number that is a multiple of two or more numbers.

Answer: 95 is the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case.

To find the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case we have to do the following steps:

    Find the LCM of 6, 15 and
    18
    Add 5 to the LCM 

Explanation:

Below is the LCM shown for 6,15 and 18 using prime factorization.

6 = 2 × 3

15 = 3 × 5

18 = 2 × 3 × 3

Thus, the LCM of 6,15 and 18 = 2 × 3 × 3 × 5 = 90

Now, adding 5 to 90, we get 90 + 5 = 95

Verification:

1) 95/6
Quotient = 15
Remainder = 5

2) 95/15
Quotient = 6
Remainder = 5

3) 95/18
Quotient = 5
Remainder = 5

Hence, 95 is the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case.

What is the least number which when divided by 6 7 8 and 9 will give a remainder of 3 in each case?

Required number = L.C.M OF 6 7 8 9 12 + 1L. C.M = 3
X 2 X 2 X 7 X 2 X 3 = 504. Hence required number = 504 +1 = 505.

What is the smallest number which when divided by 7 8 9 leaves a remainder of 2 4 6?

∴ The number is 499.

What will be the smallest number which when divided by 6 7 8 9 and 12 leaves remainder 2
Each time?

∴ 506 will be the smallest number which when divided by 6, 7, 8, 9, and 12 leaves the remainder 2 each time.

What is the least number which when divided by 5 6 7 and 8 leaves a remainder 3 but when divided by 9 leaves no remainder *?

Hence 1683 is the number which when divided by 5,6,7, and 8 leaves a remainder 3, but when
divided by 9, leaves no remainder.

What is the smallest number which has 6 8 and 12 as factor?

The smallest 3-digit number which is exactly divisible by 6,8 and 12 is 120.

What is the least number that when divided by 6 9 and 12 leaves a remainder of 5?

Hence, the least number which when divided by 6, 9, 12, 15, 18 leaves the same remainder 5 in each case, is 185.

What is the smallest number that can be divided by 6 9 and 12 without a remainder?

35 is the least number which when divided by 6,9,12 and 18 leaves no remainder.

What will be the smallest number which when divided by 6 7 8 9 and 12 leaves remainder 2 Each time?

∴ 506 will be the smallest number which when divided by 6, 7, 8, 9, and 12 leaves the remainder 2 each time.
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