USING VENN DIAGRAM TO FIND HCF AND LCM

Problem 1 :

24 = 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

a) What are the common factors of 24 and 36 ?

b) Write the common factors of 24 and 36 in the Venn diagram.

c) Using venn diagram to find the HCF and LCM of 24 and 36.

Solution :

a) Common factors of 24 and 36

2, 2 and 3 are common factors.

b)  

c)  GCF = 2 x 2 x 3 ==> 12

LCM = 2 x 2 x 2 x 3 x 3 ==> 72

Problem 2 :

Complete the Venn diagram to find HCF and LCM of 48 and 120.

Solution :

48 = 2 x 2 x 2 x 2 x 3

120 = 2 x 2 x 2 x 3 x 5

HCF = 2 x 2 x 2 x 3 ==> 24

LCM = 2 x 2 x 2 x 2 x 3 x 5 = 240

Problem 3 :

Joanne is campaigning for class president and plans to distribute some campaign materials : 20 flyers and 16 buttons. She wants each classroom to receive an identical set of campaign materials, without having any materials left over. What is the greatest number of class rooms Joanne can distribute materials to ?

Solution :

She wants to divide 20 flyers and 16 buttons.

Using factor tree, decomposing the given numbers as product of prime factors.

The common factor for 20 and 16 is 4. So, flyers and buttons should be divided into 4's, then each class will get

number of flyers = 20/4 ==> 5 flyers

number of buttons = 16/4 ==> 4 buttons

So, each class rooms will get 5 flyers and 4 buttons..

Problem 4 :

Sarena wants to create snack bags for a trip she is going on. She has 6 granola bars and 10 pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Sarena can make ?

Solution :

6 = 2 x 3

10 = 2 x 5

Here the highest common factor is 2.

We can decompose 6 granola into 2 groups. 

We can decompose the number of dried fruits into 2 groups.

Each bag should consist of

6/2 = 3 granolas and 10/2 = 5 dried fruits.

Sarena can pack 2 snack bags.

Problem 5 :

Matthew goes hiking every 12 days and swimming every 6 days. He did both kinds of exercise today. How many days from now will he go both hiking and swimming again ?

Solution :

Starting from today every 12 days after he will swim.

Days he swims = 12, 24, 36, 48, ............

Starting from today every 6 days after he will hike.

days he hike = 6, 12, 18, 24, .............

The day in which he do both is 12.