LCM and HFC

Answer :

L.C.M. of 4, 6, 8, 12 and 16 = 48
therefore Required number
= 48 + 2 = 50

Answer :

LCM of 15, 12, 20, 54 = 540
Then number = 540 + 4 = 544
[4 being remainder]

Answer :

The greatest number of five digits is 99999.
LCM of 3, 5, 8 and 12

2        3       5       8        12

2        3       5       4         6

3        3       5       2         3

          1       5       2         1

therefore LCM = 2 × 2 × 3 × 5 × 2 = 120
After dividing 99999 by 120, we
get 39 as remainder
99999 – 39 = 99960
= (833 × 120)
99960 is the greatest five digit
number divisible by the given divisors.
In order to get 2 as remainder in
each case we will simply add 2
to 99960.
therefore Greatest number
= 99960 + 2 = 99962

Answer :

LCM of 4, 5, 6, 7 and 8

=    2      4       5      6       7        8
      2      2       5      3       7        4
              1       5      3       7        2

= 2 × 2 × 2 × 3 × 5 × 7 = 840
let required number be 840 K + 2 which is multiple of 13.
Least value of K for which (840 K + 2) is divisible by 13 is K = 3
therefore Required number
= 840 × 3 + 2
= 2520 + 2 = 2522

Answer :

Required time = LCM of 252, 308 and 198 seconds

2          252        308       198
2          126        154        99
7          63          77          99
9           9           11          99
11         1           11          11
             1            1            1

therefore LCM = 2 × 2 × 7 × 9 × 11
= 2772 seconds
= 46 minutes 12 seconds