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.
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.
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