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so, any multiple of 90 will be divisible by both 45 and 30 so now we need to find out the greatest 4 digit multiple of 90.

Greatest 4 digit no=9999

On dividing 9999 by 90 we get 9 as remainder.

So the greatest 4 digit no. divisible by both 45 and 30 = 9999-9=9990