Ms. santiago has many pens in her desk drawer. she says that if you divide the total number of pens by 1 2 3 4 5 or 6 you get a remainder of 1 what is the least number of pens that could be in her drawer

No number divided by 1 leaves a remainder of 1

since every number divides evenly by 1

divided by 2 leaving a remainder of 1:

1 , 3, 5, 7, 9, all odd numbers

divided by 3 leaving a remainder of 1:

1, 4, 7, 10, 13, 16, 61

divided by 4 leaves a remainder of 1:

1 , 5, 9, 13, 17, 21, 61

divided by 5 leaves a remainder of 1:

1, 6, 11, 16, 21, 26, 31, 61

divided by 6 leaves a remainder of 1:

1, 7, 13, 19, . 61

looks like 61 , except the division by 1 part.

OR  

LCM of 2,3,4,5 is 60

to have remainder of 1 for all

60 + 1 = 61

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: