Here are some Civil Service exam exercises on GCD and LCM.

1.) What is the GCD of 8, 20, and 28?

2.) What is the GCD of 21, 35, and 56?

3.) What is 18/54 in lowest terms?

4.) What is 38/95 in lowest terms?

5.) What is the LCM of 6 and 8?

6.) What is the LCM of 5, 6, and 12?

7.) What is the product of the LCM and the GCD of 4, 8, and 20?

8.) There are 18 red marbles and 27 blue marbles to be distributed among children. What is the maximum number of children that can receive the marbles if each kid receives the same number of marbles for each color and no marble is to be left over?

9.) In a school sportsfest, there are 60 Grade 4 pupils, 48 Grade 5 pupils and 36 Grade 6 pupils. What is the largest number of teams that can be formed if the pupils in each Grade level are equally distributed and no pupil is left without a team?

10.) In a disco, the red lights blink every 3 seconds and the blue lights blink every 5 seconds. If the two colored lights blink at the same time if you turn them on, they will blink at the same time every ___ seconds.

Answers:

1.) Answer: 4

Solution:

Divisors of 8 – 1, 2, 4, 8

Divisors of 20 – 1, 2, 4, 5, 10, 20

Divisors of 28 – 1, 2, 4, 7, 14, 28

2.) Answer: 7

Solution:

Divisors of 21 – 1, 3, 7, 21

Divisors of 35 -1, 3, 5, 7, 35

Divisors of 56 -1, 2, 7, 8, 14, 28, 56

3.) Answer: 1/3

Note: Reducing fractions to lowest terms is one of the applications of GCD.

Solution:

Divisors of 18 – 1, 2, 6, 9, 18

Divisors of 54 – 1, 2, 3, 9, 18, 27, 54

Numerator = 18 divided by 18 (GCD) = 1

Denominator = 54 divided by 18 (GCD) = 3

Final answer: 1/3

4.) Answer: 2/5

Solution:

Divisors of 38 – 1, 2, 19, 38

Divisors of 95 – 1, 2, 3, 19, 95

5.) Answer: 24.

Solution:

Multiples of 6 – 6, 12, 18, 24

Multiples of 8 – 8, 16, 24

6.) Answer: 60.

Solution:

Multiples of 5 – 5, 10, 15, 20, 25, 30 … 55, 60

Multiples of 6 – 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Multiples of 12 – 12, 24, 36, 48, 60

7.) Answer: 160.

Solution

GCD of 4, 6, and 20 is 4.

LCM of 4, 6, and 20 is 40.

4 x 40 = 160.

8.) Answer: 9

Solution:

Divisors of 18 – 1, 2, 3, 6, 9, 18

Divisors of 27 – 1, 2, 3, 9, 27

9.) Answer: 12.

Solution:

Divisors of 60 – 1, 2, 3, 4, 5, 6, 10, 12, 20, 30, 60

Divisors of 36 – 1, 2, 3, 4, 6, 9, 12, 18, 36

Divisors of 48 – 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

10.) Answer: 15 seconds.

Solution

LCM of 3 and 5 is 15

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