determine two numbers nearest to 3100 which are exactly divisible by 3 5 6 8 and 20
Answers
Explanation:
The first step is identifying the least common multiple (LCM) of 7,6,5,4,3,2 which happens to be
2*3*5*7*2 = 420.
(Shortcut to LCM is directly multiply all prime numbers in the list which 2,3,5 and 7. That leaves us with 4 and 6. 4 is 2*2, there is already one 2 factored in, so factor in another 2. And 6 can be ignored as 6 = 2 *3 and both are factored in already. In short, if a number is divisible by both 2 and 3 then the number is also divisible by 6)
Now let's divide 10000/420
The quotient is 23 and the remainder is 340.
So the two numbers nearest - attention to the word nearest - not smaller, not larger - it's nearer - so the two numbers would obviously be
The highest number that is divisible by 2,3,4,5,6 and 7 and is less than 10000 which is 23*420 = 9660 and
The lowest number that is divisible by 2,3,4,5,6 and 7 and is greater than 10000 which is 24*420 = 10080
The other way to visualise this is - the nearest two numbers would definitely be the multiples of the six numbers (2,3,4,5,6,7) on either side of the given number (10000) in the number line.
So the numbers you are looking for are 9660 and 10080.