# Find the smallest number which decreased by 15 is a multiple of 125 and 225.

The smallest number which is a multiple of 125 and 225 is the l.c.m. of them.

125 = 5 × 5 × 5

225 = 5 × 5 × 3 × 3

Therefore, l.c.m.(125, 225) = 5 × 5 × 5 × 3 × 3 = 1125

Now, we have to find the smallest number which is decreased by 15.

Therefore, the required number = 1125 + 15 = 1140

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