1. I am more than 20 but less than 50.  Two of my factors are 2 and 3.  My first digit is double the second digit.  What number am I?

Between 20 and 50, 21 and 42 satisfy the given condition.

That is first digit is double  the second digit.

But 21 is not a factor of 2.

Therefore required number is 42.

2. I am a number between 49 and 50. I am a multiple of a number between 8 and 10 and also a multiple of 15.  What number am I ?

Number between 8 and 10 is 9.

Multiple of 9 between 40 and 50 is 45.

45 is a multiple of 15.

Therefore required number is 45.

3. Write the first 10 multiples of  2 and 4 and find the common multiples. 

First 10 multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

First 10 multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.

Common Multiples = 4, 8, 12, 16, 20.

4. Find the LCM of 8 and 10 using division method.

Therefore LCM = 2 × 2  ×  2  × 5 = 40. 

5. Find the LCM of 14, 18 using division method.

Therefore the LCM  = 2 × 3 × 3 × 7 = 126.

6. Find the LCM of 16, 24  using division method.

Therefore LCM = 2 × 2 × 2 × 2 × 3 = 48. 

7. Find the lowest common multiple for 14, 8.

Multiples of 4 and 4, 8, 12, 16, 20, 24, 28, - - - - -

Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, - - - - - 

Common multiples of 4 an 8 are 8, 16, 24, - - - - 

Lowest common multiples = 8

8. Find the lowest common multiple of 6 and 12.

Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, - - - - -

Multiples of 12 are 12, 24, 36, 48, - - - - -

Common multiples of 6 and 12 are 12, 24, - - - - 

Therefore Lowest common multiple = 12.

9. Find the LCM of 8 and 10 using factor tree method. 

Therefore LCM of 8 and 10 = 2 × 2 × 2 × 5

                                             = 40.

10. Find the LCM of 12 and 16 using factor tree method. 

Therefore L C M = 2 × 2 × 3 × 2 × 2 = 48.