Question

find the smallest number of six digits which divisable by 6,12,18,24
​

Answer 1

We want to determine the least six digit number, which, when divided by 6,12,18
6
,
12
,
18
and 24
24
leaves a remainder of 2
2
in each case.

First of all we would find the smallest number with this property.

Let the smallest number with this property be .
x
.

⇒−2
⇒
x
−
2
is divisible by 6,12,18
6
,
12
,
18
and 24.
24.

⇒−2
⇒
x
−
2
is the
L
C
M
of 6,12,18
6
,
12
,
18
and 24,
24
,
which is 72.
72.

So, the smallest number with this property is 72+2=74.
72
+
2
=
74.

All multiples of 72
72
to which 2
2
has been added would have this property.

Now we will find the least six digit number which is a multiple of 72.
72.
This number is 100008
100008
since 72×1388=99936,
72
×
1388
=
99936
,
which is a five digit number and 72×1389=100008,
72
×
1389
=
100008
,
which is a six digit number.

⇒
⇒
The number that we require is 100008+2=100010.