The largest 4 digit number which is exactly divisible by 18, 25 and 35. Find the smallest number by which 1008 must be. multiplied to get a perfect square. Also find the square root of square so obtained. 1225 plants are to be planted in a garden is such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

Question

The largest  4 digit number which is exactly divisible by 18, 25 and 35.  Find the smallest number by which 1008  must be.  multiplied to get a perfect square.   Also find the square root of square so obtained.                               1225 plants are to be planted in a garden is such a way that each  row contains as many plants as the number  of rows.                                        Find the number of rows and the number of plants in each row.

Reiny · Answer

18 = 2*3*3
25 = 5*5
35 = 5*7
LCM = 2*3*3*5*5*7 = 3150
how about 3150k < 9999
k < 3.1
so largest 4 digit with above properties is 3*3150 = 9450

test it with your calculator.

1008 = 2*2*2*2*3*3*7
= 16 * 9 * 7
the first two factors are perfect square, so to make the last factor a perfect square, we have to multiply by 7

so 1008*7 = 7056
check: √7056 = 84

take a run at the last one, let me know what you think.