Given below are two statements Statement I: If two numbers divided by a third number give the same remainder, their difference is exactly divisible by that number. Statement II: Least common multiple of two or more given numbers is the largest number which is exactly divisible by each of them. In light of the above statements, choose the correct answer from the options given below?

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  1. Both Statement I and Statement II are true
  2. Both Statement I and Statement II are false
  3. Statement I is true but Statement II is false
  4. Statement l is false but Statement II is true

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Option 1 : Both Statement I and Statement II are true

Calculation:

Statement 1:

Let two numbers 15 and 17 and third number be 2

When we divide 15 by 2 we get remainder 1

When we divide 17 by 2 we get remainder 1

When divided by 2 we will  get same remainder = 1

Difference in two numbers = 17 - 15 = 2

Difference of two numbers/ third number = 2/2 = 1

So, their difference is exactly divisible by third number.

Hence, Statement 1 is correct.

Statement 2: 

Let two numbers are 3 and 4

L.C.M. of 3 and 4 = 2 × 2 × 3 = 12

When we divide 12 by 3 we get 4

When we divide 12 by 4 we get 3

So, the L.C.M. is divisible by two or more numbers.

Hence, Statement 2 is correct.

∴ Both the Statement 1 and Statement 2 are true.

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