LEAST COMMON MULTIPLE AND HIGHEST COMMON FACTOR

Find the GCF and LCM of the following set of numbers. Use any method.

Problem 1 :

5, 20

GCF : _____

LCM : _____

Solution :

GCF : 

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

= 5

LCM : 

So, the least common multiple (LCM) of 5 and 20 is

= 5 × 4

= 20

Problem 2 :

14, 16

GCF : _____

LCM : _____

Solution :

GCF : 

So, the greatest common factor (GCF) of 14, 16 is  = 2

LCM : 

So, the least common multiple (LCM) of 14 and 16 is

= 2 × 7 × 8 

= 112

Problem 3 :

21, 3

GCF : _____

LCM : _____

Solution :

GCF : 

So, the greatest common factor (GCF) of 21, 3 is

= 3

LCM : 

So, the least common multiple (LCM) of 21 and 3 is 

= 3 × 7

= 21

Problem 4 :

4, 6, 24

GCF : _____

LCM : _____

Solution :

GCF : 

So, the greatest common factor (GCF) of 4, 6, 24 is 

= 2 × 2

= 4

LCM : 

So, the least common multiple (LCM) of 4, 6 and 24 is 

= 2 × 2 × 3 × 2

= 24

Problem 5 :

4, 8, 32

GCF : _____

LCM : _____

Solution :

GCF : 

So, the greatest common factor (GCF) of 4, 8, 32 is

= 2 

LCM : 

So, the least common multiple (LCM) of 4, 8 and 32 is

= 2 × 2 × 2 × 4

= 32

Multiple Choice. Read the following statements. Choose the letter of the correct answer.

Problem 1 :

What is the greatest common factor (GCF) of 16 and 24 ?

A. 6      B. 8    C. 12     D. 19

Solution :

16 = 2 × 2 × 2 × 2

24 = 2 × 2 × 2 × 3 

GCF = 2 × 2 × 2 

= 8

So, the greatest common factor (GCF) of 16 and 24 is 8.

Hence, option B. is correct.

Problem 2 :

What is the least common multiple (LCM) of 12 and 14 ?

A. 54     B. 68     C. 84     D. 146

Solution :

So, least common multiple of 2 × 2 × 3 × 7 = 84

Hence, option C. is correct.

Problem 3 :

The following numbers are common factors of 28 and 56 except ?

A. 7      B. 14      C. 8      D 28

Solution :

8 is not divisible by 28 and 56.

So, option C. is correct.

Problem 4 :

What is the greatest common factor of 14 and 56 ?

A. 7       B. 14         C. 21          D. 28

Solution :

14 = 2 × 7

56 = 2 × 2 × 2 × 7

GCF = 2 × 7

= 14

So, the greatest common factor (GCF) of 14 and 56 is 14.

Hence, option B. is correct.

Problem 5 :

What is the Least Common Multiple (LCM) of 7 and 8 ?

A. 56       B. 68      C. 84       D. 146

Solution :

So, least common multiple of 7 × 8 = 56

Hence, option A. is correct.

Problem 6 :

Which is the common factor of 24 and 32 ?

A. 8     B. 16    C. 24     D.32

Solution :

24 = 2 × 2 × 2 × 3

32 = 2 × 2 × 2 × 2 × 2

GCF = 2 × 2 × 2

= 8

So, the common factor (GCF) of 24 and 32 is 8.

Hence, option A. is correct.

Problem 7 :

What is the least common multiple of 6 and 14 ?

A.42     B. 54      C. 76      D. 84

Solution :

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

Hence, option A. is correct.

Problem 8 :

During a motorcycle race, two riders will stop to fill up the fuel tank. One does it every 4 laps, and the other every 5 laps. If they travel at the same speed, how many laps will they meet again at the fuel station ?

A. 16     B. 20     C. 25     D. 30

Solution :

The first rider will fill up the fuel in the following way,

4, 8, 12, 16, .........

The first rider will fill up the fuel in the following way,

5, 10, 15, 20, .........

The common value in both ways, the least common multiple is 

= 4 x 5

= 20

Hence, option B. is correct.

Problem 9 :

Which of the following is the greatest common factor of 28 and 36 ?

A. 4      B. 7      C. 8       D. 9

Solution :

28 = 2 × 2 × 7

36 = 2 × 2 × 3 × 3 

GCF = 2 × 2 

= 4

So, the common factor (GCF) of 28 and 36 is 4.

Hence, option A. is correct.

Problem 10 :

What is the least number of Crew that a Manager must hire if he wants to arrange them in groups of 4, 5, 6 with no Crew left ?

A. 120    B. 150       C. 60       D. 240

Solution :

So, least common multiple of 2 × 2 ×  5 × 3 = 60

Hence, option C. is correct.