Question

The smallest number of 3 digits that will take part of 12 18 24?

Answer 1

What is the smallest number of 6 digits that is exactly divisible by 18, 24, and 42?

The Lowest Common Multiple [LCM] of 18, 24 and 42 is 504, the lowest number which is divisible by 18, 24 and 42. The next number will be next multiple of 504 and so on and so forth.

Now, come to your point: the smallest number of 6 digits is 100000 when divided by 504 gives an answer of 198.41 that means a multiple of 504 near 100000 is

504 X 198 which is 99792 but it is a 5-digit number hence the next multiple of 504 which satisfies your query is 99792 + 504 =100296 which is the smallest 6-digit number that is divisible by 18, 24 and 42.

Answer 2

$\large \bf solution -$

$\bf \: Method-1$

A number which is divisible by 6,86,12 lcm, these numbers will be divisible.

LCM of 6,8,12 is 24

To find the 3-digit number smaller than 24, take a multiplier of 24

=> 24 × 1 = 24

=> 24 × 2 = 48

=> 24 × 3 = 72

=> 24 × 4 = 96

=> 24 × 5 = 120

So the smallest 3 digit number divided by 6, 8 and 12 is 120.

$\bf{Method-2}$

Prime factoring all three numbers, we have:

6 = 2 × 36 = 2 × 3

8 = 2 × 2 × 28 = 2 × 2 × 2

12 = 2 × 2 × 312 = 2 × 2 × 3

Upon finding their LCM, we get 2 × 2 × 2 × 32 × 2 × 2 × 3

That is, their LCM is 24.

Now, we want the smallest three digit number that divides all, i.e. the smallest three digit multiplier of 24

That would be 24 × 5 = 120