Math Reasoning Exercise: Set 7 - Questions 1 to 3
Question 1
When to use HCF when to use LCM
There are various real-life applications of LCM and HCF. The best way to understand these and grasp the concept of LCM and HCF is to learn via examples.
So let us take a look at a few examples which will help you understand LCM and HCF. H.C.F. :
We can use the H.C.F:
- To split things into smaller sections
- To equally distribute 2 or more sets of items into their largest grouping
- To figure out how many people we can invite
- To arrange something into rows or groups
We find L.C.M:
- In scenarios where an event is or will be repeating over and over
- To purchase or get multiple items in order to have enough.
- To figure out when something will happen again at the same time
Lets try this question
Area of 3 rectangular fields are 288, 408 and 552 sqcms respectively. A farmer decides to divide the field into blocks with same area. Find the minimum number of blocks. If the length of each block is 4cms. Find the breadth?
Solution:
Here we are dividing the blocks into smaller parts.
We need to get smaller parts.. hence HCF..
HCF of 288,408,552 =24
LXB =24
B =6
Question 2
Put A = 1, B=2, C=3 … Z = 26
CBF = 3,2 6
EBJ = 5,2,10
KBV=11, 2, 22
DES = 4,5,19
Can you observe a pattern.
3×2 = 6, 5×2=10, 11×2=22
Option D doesn’t fall in the pattern.
Hence Option D is the answer
Question 3
5,12 13 form a pythagorean triplet. The numbers satisfy the pythagoras theorem 13×13 = 12×12 + 5×5. Hence the triangle is a right angled triangle
area of right angled triangle. = 0.5 x 12 x 5 ( 5, 12 are the sides of the triangle) = 30 sq units. Since width is 10 units.. Length is 3 units. Perimeter = 2(10+3) = 26 units.