question_answer

Determine the smallest 3-digits number which is exactly divisible by 6, 8 and 12.

Answer:

The smallest number which is exactly divisible by 6, 8 and 12 is their LCM. But we have to get the smallest 3-digits number which is exactly divisible by the given numbers. Clearly, such a number is a multiple of the LCM of the given number. To find the L.C.M. of 6, 8 and 12.

2	6,	8,	12
2	3,	4,	6
2	3,	2,	3
3	3,	1,	3
	1,	1,	1

LCM \[=2\times 2\times 3\times 2=24\]

The smallest 3-digits number is 100, now 100 divided by 24

Number just greater than 100 and exactly divisible by 24

\[=100+(244)=100+20=120\]

Hence, the required number \[=120\]