Question

Determine the least 4 digit number which is exactly divisible by 6 8 and 12

Answer 1

Answer:

Step-by-step explanation:

First find the least common multiple of 6,8 and 12 =>

2|6,8,12

2|3,4,6

3|3,2,3

2|1,2,1

|1,1,1 Hence L.C.M. of 6,8 and 12 is 2×2×3×2=>24. Smallest 4 digit number is 1000. Divide it by 24 we get 16 as remainder So add 8 then the resulting number which is 1008 is divisible by 6,8 and 12. Hope it helps you.

Answer 2

Answer:

The least $4$ digit number, which is exactly divisible by $6$, $8$ and $12$ is $1008$.

Step-by-step explanation:

The Least Common Multiple (LCM) of a set of numbers can be defined as the least number, which is divisible by all of the numbers of the given set.

The given set of numbers is $6$, $8$ and $12$.

Multiples of $6$ are $\{6, 12, 18, 24, 30, 36, 42, 48, 54, 60,.....\}$.

Multiples of $8$ are $\{8, 16, 24, 32, 40, 48, 56, 64, 72, 80,.....\}$.

Multiples of $12$ are $\{12, 24 ,36 ,48, 60, 72, 84, 96, 108, 120,.....\}$.

Thus, the least common multiple of the given numbers $6$, $8$ and $12$ is $48$.

Hence, the least $4$ digit number, which is exactly divisible by $6$, $8$ and $12$ is also divisible by $48$.

It is known that the least $4$ digit number is $1000$.

The quotient when $1000$ is divided by $48$ is $20$.

Hence, the least $4$ digit number, which is divisible by $48$ can be given by,

$48\times(20+1)\\=48\times21\\=1008$

Therefore, the least $4$ digit number, which is exactly divisible by $6$, $8$ and $12$ is $1008$.