Question

in a garden the trees can be planted in group of 3,4,5 and 6 what is the least number of trees this garden can have?​

Answer 1

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.

Hope it helps you..

@Pari here...