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Find the least square number, exactly divisible by each one of the numbers:
(i) 6, 9, 15 and 20
(ii) 8, 12, 15 and 20.
To do:
We have to find the least square number which is exactly divisible by each one of the numbers
(i) 6, 9, 15, and 20
(ii) 8, 12, 15 and 20.
Solution:
(i) The smallest number divisible by 6, 9, 15 and 20 is their L.C.M.
LCM of 6, 9, 15 and 20 $= 180$
On resolving the L.C.M. as prime factors we get, $180= 2\times2\times3\times3\times5$
To make it a perfect square number we will multiply it by 5 then it becomes,
$\Rightarrow 180\times5 =2\times2\times3\times3\times5\times5 =900$
Therefore, the least square number which is exactly divisible by 6, 9, 15 and 20 is 900.
(ii) The smallest number divisible by 8, 12, 15 and 20 is their L.C.M.
LCM of 8, 12, 15 and 20 $=120$
On resolving the L.C.M. as prime factors we get, $120= 2\times2\times2\times3\times5$
To make it a perfect square number we will multiply it by $2\times3\times5$ then it becomes,
$\Rightarrow 120\times2\times3\times5 =2\times2\times2\times2\times3\times3\times5\times5 =3600$
Therefore, the least square number which is exactly divisible by 8, 12, 15 and 20 is 3600.
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