A person had a number of toys to distribute among children.At first he gave 2 toys to each child then 3 then 4 then 5 and then 6 but was always left with 1 .If he had given 7 toys to each child no tous would have been left with him.What is the smallest number of toys that he had?
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Answer:
301
Step-by-step explanation:
LCM of 2, 3, 4, 5, 6 = 60
Number of toys would be of the form 60K + 1.
This 60K + 1 must be divisible by 7.
(60 x 1) + 1 = 61, which isn't divisible by 7
(60 x 2) + 1 = 61, which isn't divisible by 7
(60 x 3) + 1 = 181, which isn't divisible by 7
(60 x 4) + 1 = 241, which isn't divisible by 7
(60 x 5) + 1 = 301, which is divisible by 7
So, the smallest number of toys that he had 301
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