LCM of 9,10,12,15 is 180
Smallest natural number to get remainder of 3 is (180 + 3) = 183
From the given data,
containers contain mixtures of milk and water as 1365 lit, 1560 lit and 1755 lit.
Biggest measure that can measure all these different quantities exactly can be given by
HCF of (1365, 1560, 1755)
That can be found as
HCF of 1365, 1755 = 195
Now, HCF of 195 and 1560 = 195
Hence, biggest measure that can measure all the given different quantities exactly is 195 lit.
Gold coins = 18000 , Silver coins = 9600 , Bronze coins = 3600
Find a number which exactly divide all these numbers
That is HCF of 18000, 9600& 3600
All the value has 00 at end so the factor will also have 00.
HCF for 180, 96 & 36.
Factors of
180 = 3 x 3 x 5 x 2 x 2
96 = 2 x 2 x 2 x 2 x 2 x 3
36 = 2 x 2 x 3 x 3
Common factors are 2x2×3=12
Therefore, Actual HCF is 1200
Gold Coins 18000/1200 will be in 15 rooms
Silver Coins 9600/1200 will be in 8 rooms
Bronze Coins 3600/1200 will be in 3 rooms
Total rooms will be (15+8+3) = 26 rooms.
Let the numbers be 3x, 4x, 5x.
Then, their L.C.M = 60x.
So, 60x=3600 or x=60.
Therefore, The numbers are (3 x 60), (4 x 60), (5 x 60).
Hence,required H.C.F=60
The smallest possible number of books = L.C.M of 5, 9 and 13.
Therefore, L.C.M of 5,9 and 13 is = 5 x 9 x 13 = 585.
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