Answer: 548

Explanation:
Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8
= 548.

Answer: 85

Explanation:
Since the numbers are co-prime, they contain only 1 as the common factor.
Also, the given two products have the middle number in common.
So, middle number = H.C.F. of 551 and 1073 = 29;
First number = 551 / 29   = 19; Third number = 1073/ 29 = 37.

Required sum = (19 + 29 + 37) = 85.

Answer: 46 minutes and 12 seconds

Explanation:
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.

Answer: 111

Explanation:
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.

Answer: 407

Explanation:
The L.C.M. of 3, 5 and 9 is 45.
Hence, the number is of the form (45a + 2).
The least value of ‘a’ for which (45a + 2) is multiple of 11 is 9.
Therefore, the number is 407.

Answer: 5 p.m

Explanation:
The L.C.M. of 12, 20 and 35 is 420. Hence, all 3 bells beep together after 420 minutes = 7 hours
Hence, the 3 bells will beep together 7 hours after 10 a.m. i.e. at 5 p.m.

Answer: 2 cm

Explanation:
The largest size of the tile is H.C.F. of 480 cm and 538 cm is 2 cm.

Answer: 74088

Explanation:
A number that is divisible by 8, 14 and 18 = L.C.M. of 8, 14 and 18 = 504
504 = 2*2*2*3*3*7
Hence, to get a perfect cube 504 should be multiplied by 3*7*7 = 147
The number is 74088.

Answer: 6 and 10

Explanation:
H.C.F. * L.C.M = product of the two numbers
H.C.F.*L.C.M = 60 = product of the two numbers
Let one of the numbers be x. The second number is (x+4)
60 = product of the two numbers = x*(x+4)
x2 + 4x – 60 = 0 = (x + 10)*(x – 6)
x = 6
Therefore, the numbers are 6 and 10.