Word Problem help!!!!!?

Question

Rank and File
The sergeant had fewer than 500 men to line up on parade. He tried arranging them in rows of three but found there was one left over. Then he tried them in rows of four, then five and six, but always there was one left over. Finally he tried them in rows of seven and, to his relief, saw that the rows were exactly even.
How many soldiers were lined up on parade?

Answer 1

The answer you seek will be one greater than a common mutiple of 3, 4, 5, and 6, although any common multiple of three and four is also a multiple of 6. Multiply all the common factors of 3, 4, 5 and 6 together. You get 3*4*5 = 60. Now look if 61 is divisible by 7. It isn't. Try next common multiple of 3,4,5,6, 120. 121 is also not divisible by seven. Repeat with 181, 241. 301 is divisible by 7. So there are 301 soldiers.
300/3 = 100
300/4 = 75
300/5 = 60
300/6 = 50

301/7 = 43.

Answer 2

3a+1=y, 4b+1=y, 5c+1=7, 6d+1=y, 7e=y and y<500;
the number y1= 7e –1, must be even and divisible by 5, that is y1= (n*10 +m)*10;
the number m*10 must be divisible by 4, that is m=2k and y1= (n*10 +2k)*10;
the number n*10+2k must be divisible by 3, that is n+2k must be divisible by 3;
if n=4, then k=4 y= 481; k=1 y=421;
if n=3, then k=3 y=361; k=0 y=301 =43*7;
481, 421, 361 are not divisible by 7;