math word problem

Question

an army of men can line up to march in rows of 1,2,3,4,5,6,7,8,9 or 10 and there is never any rows that is incomplete.  what is the smallest number of soldiers in the army?

Answer 1

I was always taught to multiply the highest powers of each prime factor. Using Arthur's list they would be 

 

2³

3²

5¹

7¹

 

which would give you 8x9x5x7 = 40x63 = 4x630 = 2x1260 = 2520

Answer 2

Find the least common multiple of 1,2,3,4,5,6,7,8,9, and 10

1

2

3

2x2

5

2x3

7

2x2x2

3x3

2x5

 

LCM=2x5x3x3x2x2x7=2520 soldiers

1 row of 2520

2 rows of 1260

3 rows of 840

4 rows of 630

5 rows of 504

6 rows of 420

7 rows of 360

8 rows of 315

9 rows of 280

10 rows of 252