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 least common multiple of 12 and 15 is
12 = 2 x 2 x 3
15 = 3 x 5
LCM of 12 and 15 is 2 x 2 x 3 x 5 = 60.
To find the greatest number which divides the numbers 964, 1238 and 1400 leaving the remainders 41, 31 and 51 is nothing but the HCF of (964 - 41), (1238 - 31), (1400 - 51).
Therefore, HCF of 923, 1207 and 1349 is 71.
LCM of 9,10,12,15 is 180
Smallest natural number to get remainder of 3 is (180 + 3) = 183
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