find the least number which divided by 2,3,4,5,6, leaves remainder of 1 in each case but when divided by 7 leaves no remaider.

Explanation

Let the number is `n`.

When `n` is divided by `2`, it leaves remainder `1`.

When `n` is divided by `3`, it leaves remainder `1`.

When `n` is divided by `4`, it leaves remainder `1`.

When `n` is divided by `5`, it leaves remainder `1`.

When `n` is divided by `6`, it leaves remainder `1`.

The remainder in each case is `1` .

`:. (n - 1)` is the `LCM` of `2, 3, 4, 5 and 6.`

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