Perfect Square : A number when written as product of prime factors , if each prime factor has even number as its power , then the number is perfect square. Writing the given number as product of prime factors 6 = 2 x 3 12 = 2³ x 3 18 = 2 x 3² 24= 2³ x 3 LCM = 2³ x 3² = 72 But 72 is not the perfect square. But multiples of 72 are also exactly divisible by given numbers. 72 x 2 =144 is the perfect square.
The Largest number of four digits is 9999. Required number must be divisible by L.C.M. of 12,15,18,27 i.e. 540. On dividing 9999 by 540,we get 279 as remainder . Required number = (9999-279) = 9720.
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