The greatest number that will divide 172,205 and 304 leaving the same remainder in each case is HCF ((205-172), (304-205), (304-172)) = HCF of 33, 99, and 132 33=31x11 99=3 x 3 x 11 132=3 x 2 x 2 x11 Required number =3 x 11=33
L.C.M. of 2, 4, 6, 8, 10, 12 is 120. So, the bells will toll together after every 120 seconds(2 minutes). In 30 minutes, they will toll together 30 + 1 = 16 times. 2
EXAMIANS