### Boy with Toffees

A boy has few toffees with him, then comes one of his friend and they decide to share them equally and they are able to divide them without any toffee remaining. Then one more friend comes and they divide the toffees in 3 equal parts, then one more friend comes, they are still able to divide the toffees in 4 equal parts, then comes one more friend, they are still able to divide them equally, similarly they are able to divide it equally in 5 and 6 equal parts but not when they are 7 and decide to divide equally they are left with one extra toffee.

**Can you tell the minimum number of toffees boy had initially ?**

Since, They are able to divide the toffees equally between 2,3,4,5 and 6 boys so the number of toffees must be a multiple of all of these.

To get the minimum number we should first get the Least Common Multiple of 2,3,4,5 and 5, i.e. 2^

Now lets divide it by 7, the remainder is = 4, so it cant be the answer, So we should try the next possible answer i.e. 120, divide it by 7, remainder = 1, so minimum number of toffees boy can have is 120.

To get the minimum number we should first get the Least Common Multiple of 2,3,4,5 and 5, i.e. 2^

^{2}.3^^{1}.5^^{1}= 60.Now lets divide it by 7, the remainder is = 4, so it cant be the answer, So we should try the next possible answer i.e. 120, divide it by 7, remainder = 1, so minimum number of toffees boy can have is 120.

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cj says

if it is divided equally when there are 2,3,4,5,6 friends then it is LCM of those numbers i.e 5*4*6=120

Gaurav k says

@cj LCM is not correct ,, http://www.calculatorsoup.com/calculators/math/lcm.php it should be 60 for 2,3,4,5,6