two milk tankers contain 450 liters of milk respectively.find the maximum capacity of a container which can measure the milk of both the tankers when used and exact number of times
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Two milk tankers contain 450 litres and 600 litres of milk respectively. Find the maximum capacity of a container which can measure the milk of both the tankers when used an exact number of times.
Solution: To find maximum capacity of a container, we will find the HCF of 450 and 600.
2
450, 600
3
225, 300
5
75, 100
5
15, 20
3, 4
HCF = 2 x 3 x 5 x 5 = 150
Therefore, maximum capacity of the required container is 150 litres. It will fill the first container in 450 ÷ 150 = 3 and the second in 600 ÷ 150 = 4 refills.
Example 2: Find the least number which when divided by 12, 15, 18 and 20 leaves a remainder 5 in each case.
Solution: Here, we will find LCM of 12, 15, 18 and 20.
2
12, 15, 18, 20
2
6, 15, 9, 10
3
3, 15, 9, 5
3
1, 5, 3, 5
5
1, 5, 1, 5
1, 1, 1, 1
Thus, LCM = 2 x 2 x 3 x 3 x 5 = 180
180 is the least number which when divided by the given numbers will leave remainder 0 in each case.
Therefore, the required number is 5 more than 180. The required least number = 180 + 5 = 185
Example 3: Find the smallest 4 digit number which is divisible by 18, 24 and 32.
Solution: Here, we will find LCM of 18, 24 and 32.
2
18, 24, 32
2
9, 12, 16
2
9, 6, 8
2
9, 3, 4
2
9, 3, 2
3
9, 3, 1
3
3, 1, 1
1, 1, 1
Thus, LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288
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