Find the smallest 4 digit number which is divisible by 18 24 and 32

Compute the required value. Factors of 18 , 24 and 32 are 18 = 2 × 3 × 3 24 = 2 × 2 × 2 × 3 32 = 2 × 2 × 2 × 2 × 2 Thus the L.C.M. of 18 , 24 and 32 is 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288. To get the smallest four digit number that is divisible by 288, we have to write the multiples of 288 . 288 × 2 = 576 288 × 3 = 864 288 × 4 = 1152 Hence 1152 is the smallest 4 digit number divisible of 18 , 24 and 32.

Actually, divisibility by 7 & 8 is quite easy once you get the hang of it. First, I will talk about divisibility by 8, since it is easier. In order to test this, you only must check to see whether the last three digits of the number are divisible by 8. If they are, then the entire number is divisible by 8 too. Example 1: Is the number 8347475537272 divisible by 8? Answer 1: Yes, because the last 3 digits, 272, are divisible by 8. Example 2: Is the number 314159265358979323846 divisible by 8? Answer 2: No, because the last 3 digits, 846, are not divisible by 8. Next, divisibility by 7. This one is a little weird but it really is quite simple after you practice it a couple of times. In order to test this, you must take the last digit of the number you’re testing and double it. Then, subtract this number from the rest of the remaining digits. If this new number is either 0 or if it’s a number that’s divisible by 7, then then original number is divisible by seven. (You may have to repeat this a couple of times if the divisibility of the resulting number is not immediately obvious). Example 1: Is the number 364 divisible by 7? Answer 1: Yes: Double the 4 to get 8. Subtract 8 from 36 to get 28. Since 28 is divisible by 7, we can now say for certain that 364 is also divisible by 7. Example 2: Is the number 8256 divisible by 7? Answer 2: No, Double 6 to get 12. Subtract 12 from 825 to get 813. 813 is slightly too large to tell whether it is divisible by 7 so we must repeat the pro...