H.C.F. AND L.C.M. OF NUMBERS- EXERCISE 2 ( SOLUTIONS: 71 TO 75:)

71. L.C.M. of 5, 6, 7, 8= 840.

       Required number = (840 x  2 + 3 ) = 1683.

72. L.C.M. of 16, 18, 20, 25 =3600. Required number is of the form 3600 k + 4.

       Least value of k for which (3600 k + 4) is divisible by 7 is k = 5.

       Required number = (3600 x 5 + 4) = 18004.

73. L.C.M. of 2, 4, 8, 10, and 12 is 120.

         So, the bells will toll together after every 120 seconds, i.e., 2 minutes.

         In 30 minutes, they will toll together [(30/2) + 1)] =16 times.

74. Interval after which the devices will beep together

      = (L.C.M. of 30, 60, 90, 105) mi. = 1260 min. = 21  hrs.

      So, the devices will again beep together 21 hrs. after 12 noon I;e., at 9 a.m.

75. L.C.M. of 252, 308 and 198 = 2772.

        So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.