Question

Could someone give examples for HCF and LCM. I'm unable to comprehend, when to take out HCF and when LCM. Please help, with difficult examples.

Answer 1

58,78
58=1.2.29
78=1.2.13.3
h.c.f=1.2.=2
l.cm=1.2.29.13.3=2262

Answer 2

LCM or Lowest Common Multiple is the smallest Integer that is as well as a multiple of the given Numbers.

Example: What is the LCM of 2 and 3?
It is 6 because $2(3)$=$3(2)$=6

It is used not very commonly.

Word Problem: Sammy is playing on a Merry-Go-Round. $\frac{1}{3}$ the people behind him plus $\frac{3}{4}$ the people in front of him plus 1 equals the number of total people on the merry-go-round . How many people are there in the Merry-Go-Round?

Answer:
There are 13 people on the Merry-Go-Round.

Why?
We know  $\frac{1}{3}$ of the people behind him plus $\frac{3}{4}$ in front of him plus one is the total amount.

You cannot make a portion of a person! So we know that the number of people ahead of him is a multiple of 4 and the number of people behind him is a multiple of 3.

Find the LCM of 3 and 4.

$LCM_{3,4} +1=w$

LCM of 3 and 4 is 12.

$12+1=13$

So the total number of people on the merry go round $=13$
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HCF or Highest Common Factor is the greatest integer which is also a factor of the given numbers.

For Example, find the HCF of 4 and 6.

Factors of 4: $1,2,4$
Factors of 6: $1,2,3,6$

Find the common Factors.
They are 1 and 2. 2 is bigger than 1, so the HCF of 4 and 6 is 2.

Word Problem:Simplify the fraction $\frac{12}{30}$

Answer:
$\frac{2}{5}$

Why:
We know that the HCF of 12 and 30 is 6.
Now divide 12 and 30 by 6.

We will get 2 and 6. 
So $\frac {12}{30}=\frac{2}{5}$
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Hope it helps.