True Magical Number

Puzzle # 13

A Very Magical Number(Dividend) that leaves a reminder that is one less than number(Divisor) that was used to perform the division

• When Magical Number(Dividend) divided by 2 leaves Reminder 1.
• When Magical Number(Dividend) divided by 3 leaves Reminder 2.
• When Magical Number(Dividend) divided by 4 leaves Reminder 3.
• When Magical Number(Dividend) divided by 5 leaves Reminder 4.
• When Magical Number(Dividend) divided by 6 leaves Reminder 5.
• When Magical Number(Dividend) divided by 7 leaves Reminder 6.
• When Magical Number(Dividend) divided by 8 leaves Reminder 7.
• When Magical Number(Dividend) divided by 9 leaves Reminder 8.
• When Magical Number(Dividend) divided by 10 leaves Reminder 9.

What is the Magical Number (Dividend) ??
Magical Number is not very small neither too big. Think of it!!


Solution
In all the above specified conditions, Common thing to observe is every time when Magical Number (dividend) is divided by a particular number yields a reminder that is 1 less than the particular number.

From our basic Math, we know that Least common multiple satisfying above all condition will yield a reminder Zero. and LCM for 1,2,3,4,5,6,7,8,9,10 is 

Required Magical Number = LCM -1 
                                        = 2520 - 1
                                        = 2519


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