Question

I have a certain no.of beads with me which lie between 600 and 900 .If two beads are taken away the remainder can be equally divided among 3 4 5 6 7 or 12 boys . the no.of beads i have is.....?

Answer 1

Let the number of beads be x.
When 2 beads are taken, the remaining are x-2.
Now these x-2 beads can be equally divided between 3,4,5,6,7 and 12 people, therefore x-2 is the LCM of these numbers between 598 and 890.
Now LCM of these numbers is 840, which satisfies our conditions.Thus
$x - 2 = 840 \\ x = 842$
Thus the number of beads is 842!