LCM AND GCF PROBLEMS

Problem 1 :

The greatest common factor (GCF) of 24 and 72 is ____.

A. 3      B. 13      C. 23     D. 24

Solution :

24 = 2 × 2 × 2 × 3

72 = 2 × 2 × 2 × 3 × 3

GCF = 2 × 2 × 2 × 3

= 24

So, the greatest common factor (GCF) of 24 and 72 is 24.

Hence, option D. is correct.

Problem 2 :

Find the set of numbers which has the GCF and LCM for the set.

Solution :

To find GCF, we have to divide all the numbers using particular times tables.

Considering option A. 9, 21 is divisible by 3. But 32, 41 is not divisible by 3.

So, we decide all the numbers is not divisible particular times tables.

The GCF and LCM will not be one of the values in option A. 

7 = 7

21 = 3 × 7

42 = 2 × 3 × 7

GCF = 7

So, the greatest common factor (GCF) of 7, 21, 42 is 7.

So, least common multiple of 7 × 3 × 2 = 42

Hence, option C. is correct.

Problem 3 :

The LCM of 8, 12, and 24 is _____.

A. 36      B. 28    C. 26       D. 24

Solution :

So, least common multiple of 2 × 2 × 2 × 3  = 24 

Hence, option D. is correct.

Problem 4 :

Allan wants to cut a 60 cm long and 90 cm long stick into the same length for his project. What is the length of that piece of sticks ?

A. 20 cm       B. 30 cm    C. 40 cm     D. 50 cm

Solution :

Length of the sticks = 60 cm and 90 cm

Greatest common factor is 2 x 3 x 5 = 30

So, length of each piece of stick is 30 cm. Option B.

Problem 5 :

The greatest common factor of 18 and 12 is _____.

A. 12      B. 18      C. 6      D. 9

Solution :

18 = 2 × 3 × 3

12 = 2 × 2 × 3

GCF = 2  × 3

= 6

So, the greatest common factor (GCF) of 18 and 12 is 6.

Hence, option C. is correct.

Problem 6 :

If the LCM of a set of number is 24. What are the numbers ?

A. 7 and 8        B. 6 and 9       C. 3 and 6     D. 4 and 5

Solution :

3 and 6 is divisible by 24.

So, least common multiple of 2 × 2 × 2 × 3  = 24 

Hence, option C. is correct.

Problem 7 :

The LCM of 9 and 6 is _____.

A. 36       B. 18      C. 42     D. 21

Solution :

So, least common multiple of 3 × 3 × 2 = 18

Hence, option C. is correct.

Problem 8 :

The GCF of 24 and 36 is _____.

A. 12       B. 8     C. 6       D. 4

Solution :

24 = 2 × 2 × 2 × 3

36 = 2 × 2 × 3 × 3

GCF = 2 × 2 × 3 

= 12

So, the greatest common factor (GCF) of 24 and 36 is 12.

Hence, option A. is correct.

Problem 9 :

What is the LCM of 12, 7, and 3 ?

A. 273        B. 252        C. 127             D. 84

Solution :

So, least common multiple of 3 × 4 × 7 = 84

Hence, option D. is correct.

Problem 10 :

What pair of numbers between 110 and 140 have 17 as their GCF ?

Solution :

119 = 7 × 17

136 = 2 × 2 × 2 × 17

GCF = 2 × 2 × 3 

= 17

So, the greatest common factor (GCF) of 119 and 136 is 17.

Hence, option B. is correct.

A. Use the continuous division to find the GCF of each pair of numbers.

Problem 11 :

The GCF of 12 and 20 = _____

Solution :

GCF = 2 × 2

= 4

So, the greatest common factor (GCF) of 12 and 20 is 4.

Problem 12 :

The GCF of 20 and 35 = _____

Solution :

GCF = 5

So, the greatest common factor (GCF) of 20 and 35 is 5.

Problem 13 :

15 and 9

GCF = _____

Solution :

15 = 3 × 5

9 = 3 × 3

GCF = 3

So, the greatest common factor (GCF) of 15 and 9 is 3.

Problem 14 :

8 and 40

GCF = _____

Solution :

8 = 2 × 2 × 2

40 = 2 × 2 × 2 × 5

GCF = 8

So, the greatest common factor (GCF) of 8 and 40 is 8.

Problem 15 :

16 and 48

GCF = _____

Solution :

16 = 4 × 4

48 = 4 × 4 × 3

GCF = 4 × 4

= 16

So, the greatest common factor (GCF) of 16 and 48 is 16.

Write all the factors of the set of numbers and find the GCF.

Problem 16 :

28 and 48

28 : _____

48 : _____

GCF : _____

Solution :

28 = 2 × 2 × 7

48 = 2 × 2 × 2 × 2 × 3

GCF = 2 × 2

= 4

So, the greatest common factor (GCF) of 28 and 48 is 4.

Problem 17 :

16 and 32

16 : _____

32 : _____

GCF : _____

Solution :

16 = 2 × 2 × 2 × 2

32 = 2 × 2 × 2 × 2 × 2

GCF = 2 × 2 × 2 × 2

= 16

So, the greatest common factor (GCF) of 16 and 32 is 16.

Problem 18 :

8 and 12

8 : _____

12 : _____

GCF : _____

Solution :

8 = 2 × 2 × 2 

12 = 2 × 2 × 3

GCF = 2 × 2 

= 4

So, the greatest common factor (GCF) of 8 and 12 is 4.

Problem 19 :

8, 12 and 16

8 : _____

12 : _____

16 : _____

GCF : _____

Solution :

8 = 2 × 2 × 2 

12 = 2 × 2 × 3

16 = 2 × 2 × 2 × 2

GCF = 2 × 2 

= 4

So, the greatest common factor (GCF) of 8, 12 and 16 is 4.

Problem 20 :

6, 24 and 36

6 : _____

24 : _____

36 : _____

GCF : _____

Solution :

6 = 2 × 3

24 = 2 × 2 × 2 × 3

36 = 2 × 2 × 3 × 3

GCF = 2 × 3

= 6

So, the greatest common factor (GCF) of 6, 24 and 36 is 6.