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.
Smallest number of five digits is 10000. Required number must be divisible by L.C.M. of 16,24,36,54 i.e 432, On dividing 10000 by 432,we get 64 as remainder. Required number = 10000 +( 432 – 64 ) = 10368.
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