Question

What is the lowest number that must be added to 2000 so that the sum is divisible exactly by 10,12,16,18

Answer 1

Answer:

160.

Step-by-step explanation:

Smallest number divisible by 10,12,16,18 can be given by taking lowest common factor of 10,12,16,18.

• 10 = 2 * 5

• 12 = 2 * 2 * 3

• 16 = 2 * 2 * 2 * 2

• 18 = 2 * 3 * 3

LCM = 2 * 2 * 2 * 2 * 5 * 3 * 3

LCM = 720

Here, let a number x & y so that they satisfy a relation between 2000 and 720.

2000 + y = 720x

2000 + y = 720(3) { as 720(2)<2000}

2000 + y = 2160

y = 2160 - 2000

y = 160

2160 is exactly divisible by 720( or, 10,12,16,18), and 2000 is lesser than 2160 by 160, so if 160 is added to 2000 it becomes 2160 and 2160 is divisible by 720.