What is the least number which, when divided by 52, leaves remainder 33, and when divided by 78 leaves remainder 59, and when divided by 117 leaves remainder 98?

Given, x mod 52 = 33
x mod 78 = 59
and x mod 117 = 98
In all the three cases if 19 is added to the remainders, x becomes divisible by the numbers given. Thus, we can say that x+19 is divisible by 52,78 and and 117. The lowest value of x + 119 that is divisible by these numbers is equal to the L.C.M of 52,78 and 117.
L.C.M(52,78,117) = 468
Thus, the minimum value of x = 468 - 19 = 449.

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