# H.C.F and L.C.M Aptitude Test Paper 3

11) The LCM of two numbers is 8919, and their sum is 1000. The two numbers are:

1. 993 and 7
2. 989 and 11
3. 991 and 9
4. 987 and 13

Explanation:

Let the two numbers be x and (1000 - x)

∴ x * (1000 - x) = 8919
1000x - x2 = 8919
-x2 + 1000x -8919 = 0
-x2 + ( 991 + 9)x - 8919 = 0
-x2 + 991x +9x - 8919 = 0
-x(x - 991) + 9(x - 991) = 0
(x - 991) (-x + 9) = 0

∴ (x - 991) = 0
X = 991, and
(-x + 9) = 0
-x = -9
X = 9
So, the required numbers are 991 and 9.

12) If the LCM of two numbers is 70 and their HCF is 2, find the numbers.

1. 2, 35
2. 6, 70
3. 4, 70
4. 14, 10

Explanation:

Apply Formula: HCF x LCM = First number x Second number
2 x 70 = 140 (product of two numbers)
The option D satisfies the given condition, as 14 * 10 = 140. So, the required numbers are 14 and 10.

13) Three different containers contain 496 liters, 403 liters, and 713 liters of water, respectively. What is the capacity of the biggest container that can measure three different quantities evenly?

1. 1 liter
2. 7 liters
3. 31 liters
4. 41 liters

Explanation: For the capacity of the biggest container, we have to find the HCF.
HCF: By Long Division method
First find the HCF of two numbers, 496 and 403 The HCF of 496 and 403 = 31
Now find the HCF of 31 and 713 HCF of 713 and 31 is 31
So, the maximum capacity is 31 liters.

14) The least number which when divided by 2, 3, 4, 5 and 6 leaves the same remainder 1 in each case. If the same number is divided by 7, it leaves no remainder. Find the number.

1. 231
2. 301
3. 371
4. 441

Explanation:

LCM of 2, 3, 4, 5, 6 LCM = 2 x 2 x 3 x 5 = 60

Now, 60 x 1 + 1 = 61 is not divisible by 7

60 x 2 + 1 = 121 is not divisible by 7

60 x 5 + 1 = 301 is divisible by 7

Hence 301 is the number.

15) Which is the greatest three-digit number which when divided by 6, 9 and 12 leaves a remainder of 3 in each case?

1. 975
2. 996
3. 939
4. 903

Explanation:

Greatest three digit number = 999
LCM of 6, 9 and 12 LCM = 2 x 2 x 3 x 3 = 36

On dividing 999 by 36,

Remainder = 27.

∴ The greatest three digit number divisible by 6, 9, and 12

= (999 - 27) = 972

As per the question, the required number is (972 + 3) = 975.

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