51. Required number of students =
H.C.F. of 1001 and 910 = 91
52. Largest size of the tile = H.C.F.
of 378 cm and 525 cm = 21 cm.
53. REQUIRED NUMBER = H.C.F. Of (91 – 43), (183 – 91) and (183 – 43)
=
H.C.F. of 48, 92 and 140 = 4
54. N = H.C.F. of (4665 – 1305), (6905
– 4665) and (6905 – 1305)
= H.C.F of 3360, 2240 and 5600 = 1120.
Sum of digits in N= (1+ 1 + 2 + 0) =
4.
55. Required number = H.C.F of (1356 – 12), (1868
– 12) and (2764 -12)
H.C.F. of 1344, 1856 and 2752 = 64.
56. Required number = H.C.F. of (1657
– 6) and (2037 – 5)
H.C.F. of 1651 and 2032 =127.
57. L.C.M. of 8, 16, 40 and 80 = 80.
8/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80.
Since, 70/80 > 63/80> 65/80 > so 7/8 > 63/80 > 13/16>
31/40.
So, 7/8 is the largest.
58. L.C.M. of 12, 18, 21, 30
= 2 x 3 x 2 x 3 x 7 x 5 = 1260.
Required number = (1260 /2) = 630.
59. Required fraction = L.C.M. of 6/7,
5/14, 10/21 = L.C.M. of 6, 5, 10 = 30
H.C.F. of 7, 14, 21
60. Least number of 5 digits is
10000.L.C.M of 12, 15 and 18 is 180.
On dividing 10000 by 180, the remainder is 100.
Required number = 10000 + (180 -100) = 10080.
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