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Byju's Answer
Standard IX
Mathematics
Introducing Large Numbers
Find the H.C....
Question
Find the H.C.F and L.C.M of the following by the fundamental theorem of arithmetic.
(i) 9 and 12
(ii) 60 and 72
(iii) 8624 and 21658
(iv) 12, 30, 144
(v) 17, 13, 29
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Solution
(
i
)
9
=
3
×
3
=
3
2
12
=
2
×
2
×
3
=
2
2
×
3
1
HCF
of
9
and
12
=
3
1
=
3
LCM
of
9
and
12
=
2
2
×
3
2
=
4
×
9
=
36
(
ii
)
60
=
2
×
2
×
3
×
5
=
2
2
×
3
1
×
5
1
72
=
2
×
2
×
2
×
3
×
3
=
2
3
×
3
2
HCF
of
60
and
72
=
2
2
×
3
1
=
2
×
2
×
3
=
12
LCM
of
60
and
72
=
2
3
×
3
2
×
5
1
=
8
×
9
×
5
=
360
(
iii
)
8624
=
2
×
2
×
2
×
2
×
7
×
7
×
11
=
2
4
×
7
2
×
11
21658
=
2
×
7
×
7
×
13
×
17
=
2
1
×
7
2
×
13
×
17
HCF
of
8624
and
21658
=
2
1
×
7
2
=
2
×
49
=
98
LCM
of
8624
and
21658
=
2
4
×
7
2
×
11
×
13
×
17
=
16
×
49
×
11
×
13
×
17
=
1905904
(
i
v
)
12
=
2
×
2
×
3
=
2
2
×
3
1
30
=
2
×
3
×
5
=
2
1
×
3
1
×
5
1
144
=
2
×
2
×
2
×
2
×
3
×
3
=
2
4
×
3
2
HCF
of
12
,
30
and
144
=
2
×
3
=
6
LCM
of
12
,
30
and
144
=
2
4
×
3
2
×
5
1
=
720
(
v
)
17
=
17
1
×
1
23
=
23
1
×
1
29
=
29
1
×
1
HCF
of
17
,
23
and
29
=
1
LCM
of
17
,
23
and
29
=
17
×
23
×
29
=
11339
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