Determine the smallest 6 digit number which is exactly divisible by 8,15,and21

Find the least common multiple of 8, 15, and 21. . . . . . It's 280 .

So all the numbers divisible by 8, 15, and 21 are all the multiples of 280.

The smallest 6-digit number is 100,000 .

100,000 / 280 = 357.1 , so the next whole-number multiple is the 358th one.

280 x 358 = 100,240 .

You can tell right away that this is the smallest one that qualifies,
because if you take away 280 and go to the next smaller multiple,
it won't have 6 digits anymore.