What is the smallest integer greater than 1 that leaves a remainder of 1 when divided by any of the integers 6,8 and 10?

It leaves a remainder of 3

that means is it NOT a multipule of 6 or 8 or 10

it has to be more than 10 though

6x+1=8y+1=10z+1

subtract 1 from everybody

6x=8y=10z

so basically what is the least common multplule and then add 1

LCM

factor

6=2*3

8=2*2*2

10=2*5

therefor the LCM=2*2*2*3*5=120

then add 1

120+1=121

the smallest intege is 121