Joshua has more than 250 toy soldiers.

Question

Joshua has more than 250 toy soldiers. when he tries to arrange them in rows of 3, there are 2 left over when he tries to arrange them in rows of 5 there are 2 left over. when he tries to arrange them in rows of 7 there are 2 left over. what is the least number of toy soldiers Joshua may have.

Answer 1

317

Three hundred seventeen

We need three QUOTIENTS, , X,Y, and Z such that

3x+2 = 5y+2 = 7z+2 > 250

3x = 5y = 7z

The least common multiple of 3,5, and 7 is 105.

3 * 105 = 315

315/5 = 63

315/7 = 45

So there are 105 rows of 3 with 2 left over, which makes 317

there are 63 rows of 5 with 2 left over, which makes 317

there are 45 rows of 7 with 2 left over , which makes 317.