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Byju's Answer
Standard XII
Mathematics
Compound Statement
If p and ...
Question
If
p
and
q
are positive integers such that L.C.M of p & q is
360
and the total possible number of ordered pairs
(
p
,
q
)
is N, then the remainder when
N
is divided by
6
, is
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Solution
360
=
2
3
×
3
2
×
5
Let
p
=
2
a
×
3
b
×
5
c
,
q
=
2
d
×
3
e
×
5
f
p
q
=
360
=
2
a
+
d
3
b
+
e
5
c
+
f
⇒
a
+
d
=
3
,
a
,
d
≥
0
⇒
b
+
e
=
2
,
b
,
e
≥
0
⇒
c
+
f
=
1
,
c
,
f
≥
0
No. of solutions of
a
+
d
=
3
is
3
+
2
−
1
C
2
−
1
=
4
No. of solutions of
b
+
e
=
3
is
2
+
2
−
1
C
2
−
1
=
3
No. of solutions of
c
+
f
=
3
is
1
+
2
−
1
C
2
−
1
=
2
⇒
Total possibilities
=
4
×
3
×
2
=
24
=
N
⇒
N
6
=
24
6
=
4
∴
Remainder
=
0.
Hence, the answer is
0.
Suggest Corrections
0
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