Question

Find a 4-digit number with each of the following properties. All of its digits are different. It is divisible by 2, 3, 4, 5, 6, 8, 9, and 10. It is greater than 2000 but less than 3000

Answer 1

Answer:

2160 is the answer

Answer 2

Answer:

2160

Step-by-step explanation:

Prime Factorization of 2 shows:

2 is prime  =>  $2^{1}$

Prime Factorization of 3 shows:

3 is prime  =>  $3^{1}$

Prime Factorization of 4 is:

2 x 2  =>  $2^{2}$

Prime Factorization of 5 shows:

5 is prime  =>  $5^{2}$

Prime Factorization of 6 is:

2 x 3  =>  $2^{1}$ × $3^{1}$

Prime Factorization of 8 is:

2 x 2 x 2  =>  $2^{3}$

Prime Factorization of 9 is:

3 x 3  =>  $3^{2}$

Prime Factorization of 10 is:

2 x 5  =>  $2^{1}$ × $5^{1}$

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

$2^{1}, 2^{1}, 2^{1}, 3^{1}, 3^{1}, 5^{1},$

Multiply these factors together to find the LCM.

LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360

360 × 6 = 2160