HCF and LCM ( 21 to 25 )

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Questions:

21. Three different containers contain 465 liters, 372 liters and 682 liters of mixtures of milk and water respectively. What will be the biggest measure which can measure all the different quantities exactly?

A)    1 liter

B)     7 liters

C)    31 liters

D)    41 liters

E)    None of these

View Answer

Answer: option (C)

Explanation:

HCF of (465, 372 and 682) = 31

Required Measurement = 31 litres.

22. The greatest number which when divided by 1013 and 1351 leaves remainder 5 and 7 respectively is:

A)    24

B)    8

C)    16

D)    32

E)    None of these

View Answer

Answer: option (A)

Explanation:

HCF of (1013 – 5) and (1351 – 7)

HCF of (1008) and (1344) = 24

23. The HCF of two numbers is 12 and their difference is 12. The numbers are:

A)    66, 78

B)    70, 82

C)    94, 106

D)    84, 96

E)    None of these

View Answer

Answer: option (D)


Explanation:

HCF of (84, 96) = 2 * 2* 3 = 12

Difference of (84, 96) = 12

So, out of the given numbers the two with HCF 12 and difference 12 are 84 and 96.

24. The product of the LCM and HCF of two numbers is 24. The difference of two numbers is 2. Find the numbers.

A)    2 and 4

B)    6 and 4

C)    8 and 6

D)    8 and 10

E)    None of these

View Answer

Answer: option (B)

Explanation:

Let the numbers be y and (y + 2). Then, y (y + 2) = 24

  • y2 + 2y– 24 = 0
  • (y – 4) (y + 6) = 0
  • y = 4

So, the numbers are 6 and 4.

25. Three numbers are in the ratio 3:4:5 and their LCM are 2400. Their HCF is:

A)    40

B)    80

C)     120

D)    200

E)    None of these

View Answer

Answer: option (A)

Explanation:

Let the numbers be 3x, 4x and 5x. Then, their LCM = 60x.

So, 60x = 2400 or x = 40.

∴ The numbers are (3 * 40), (4 * 40) and (5 * 40).

Hence, required HCF = 40.

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