Question

Determine the two numbers nearest to 10000 which is exactly divisible by 2, 3,4,5,6 and 7.

Answer 1

Solution: Step 1: Take the LCM of given numbers. LCM of (1, 2, 3, 4, 5, 6 and 7 ) = 420 Step 2: Divide 10000 by 420, in which the value comes nearest to 10000 When 420 is divided by 23, it gives a remainder of 340 Step 3: Subtract 340 from 10000 = 10000 - 340 = 9660 Therefore, 9660 is the first number which is nearest to 10000 and divisible by 1, 2, 3, 4, 5, 6 and 7. Step 4: Multiply 420 by 24 to get the second nearest number 420 * 24 = 10080 Therefore, the two numbers are 9660 and 10080

Answer 2

Step-by-step 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.