Question

find the smallest 4 digit number which is divisible by 6,8,9​

Answer 1

Step-by-step explanation:

Find the LC.M. of 6,8 and 9.

2 |6,8,9

2 |3,4,9

3 |3,2,9

3 |1,2,3

2 |1,2,1

|1,1,1. So the least common multiple of 6,8,9 is 2×2×3×3×2 =>72. Now the smallest four digit number is 1000. divide it by 72 we get 13 as quotient and 64 as remainder so add 8 to 1000 then 1008 is the smallest 4 digit number divisible by 6,8 and 9. Hope it helps you.

Answer 2

Answer:

The smallest 4 digit number which is divisible by 6,8,9​ is 1008.

Step-by-step explanation:

• To find the smallest 4 digit number which is exactly divisible by 6,8,9, first  we find the LCM of the three integers 6,8 and 9

6=2×3

8=2×2×2

9=3×3

LCM=2×2×2×3×3=72

• 72 is the smallest two digit number which is divisible by the given integers.

• But we want the least 4 digit number, which is exactly divisible by  6,8,9 .

• Smallest four digit number is 1000

        [1000 ÷ 72]= (13 × 72) + 64

         Remainder =64

• We need to find a number where the remainder is 0

• Required number=1000+(72 - 64) = 1000 + 8 = 1008

• 1008 is the smallest 4 digit number divisible by the given numbers 6,8,9​.