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Byju's Answer
Standard X
Mathematics
Euclid's Division Algorithm
Find the leas...
Question
Find the least number that is divisible by all the numbers between
1
and
10
(both inclusive).
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Solution
The least number that is divisible by
(
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
)
we have to take
L
C
M
of given numbers.
As all number are divisible by
1
, than
we neglect if
using prime factors
2
=
2
,
3
=
3
,
4
=
2
×
2
,
5
=
5
6
=
2
×
3
,
7
=
7
,
8
=
2
×
2
×
2
,
9
=
3
×
3
,
10
=
2
×
5
Now
L
C
M
of given number is
=
2
×
2
×
2
×
3
×
3
×
5
×
7
×
=
8
×
9
×
35
L
C
M
=
2520
∴
2520
is least number divisible by
(
1.....10
)
both inclusive.
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