a Gardiner has to plant trees in rows no.of trees.if he plants in row of 6'8'10'12 then 5 trees are left umplanted but if he plants in row of trees each,then no tree is left what is the no.of trees that the Gardiner plants
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Solution :-
L.C.M. of 6, 8, 10 and 12
6 = 2*3
8 = 2*2*2
10 = 2*5
12 = 2*2*3
L.C.M. of 6, 8, 10 and 12 = 2*2*2*3*5 = 120
When equal number of trees are planted in rows of 6, 8, 10 or 12, five trees are left unplanted.
Hence, number of trees will be (120x + 5), which must be divided by 13 as per the given condition in the question.
By hit and trial method =
(120x + 5)/13 will be satisfied for x = 7
(120*7) + 5
So, total number of trees = 840 + 5 = 845
845 is exactly divisible by 13.
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