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1. From a basket of mangoes when counted...

1. From a basket of mangoes when counted in twos there was one extra, counted in threes there were two extra, counted in fours there were three extra, counted in fives there were four extra, counted in sixes there were five extra. But counted in sevens there were no extra, Atleast how many mangoes were there in the basket?

Text Solution

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Let the number of mangoes be `n`.
When `n` is divided by `2`, it leaves remainder `1`.
When `n` is divided by `3`, it leaves remainder `2`.
When `n` is divided by `4`, it leaves remainder `3`.
When `n` is divided by `5`, it leaves remainder `4`.
When `n` is divided by `6`, it leaves remainder `5`.
The remainder in each case is `1` less than the divisor.
`:. (n + 1)` is the `LCM` of `2, 3, 4, 5 and 6.`
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