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A gardener has to plant trees in rows containing equal number of trees. If he plants in rows of 6, 8, 10 or 12 then five trees are left unplanted. But if he plants in rows of 13 trees each, then no tree is left. What is the number of trees that the gardener plants ?

A gardener has to plant trees in rows containing equal number of trees. If he plants in rows of 6, 8, 10 or 12 then five trees are left unplanted. But if he plants in rows of 13 trees each, then no tree is left. What is the number of trees that the gardener plants ? Correct Answer 845

LCM of 6, 8, 10, 12 = 120
∴ Required number is of the from 120k + 5
Least value of k for which (120k + 5) is divisible by 13 is k = 7
∴ Required number
= (120 × 7 + 5)
= 845

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