Question

Find the smallest number which when divided by 7, 11 and 13 leaves remainder of 6, 10 and 12 respectively​

Answer 1

Step-by-step explanation:

7*6=42+ 6=48

48 divided by 7 gives 6 remainder Similarly,

11*10=110+10=120

&

13*12=156+12=168

48=2*2*3*2*2

120=2*3*2*5*2

168=2*2*3*7

LCM = 2*2*3=12

48 is smallest number

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Answer 2

The required number is 1000.

Given :

7, 11 and 13 leaves remainder of 6, 10 and 12 respectively

To find :

The smallest number which is divided by 7,11 and 13

Solution :

The L.C.M ( Lowest Common Multiple ) of 7, 11 and 13 is

= 7 × 11 × 13 ( Since they have no common factor )

= 1001

Now, the difference between the actual numbers and their respective remainders :

=> 7-6 = 11-10 = 13-12 = 1

Hence, the smallest number which when divided by 7, 11 and 13 leaves remainder of 6, 10 and 12 respectively is 1001 - 1

= 1000.

Therefore, the required number is 1000.

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