HCM and LCM
Factors
A factor of a number are all those numbers, which exactly divide the given number. “Exactly divides” means that when a number is divided by its factor the reminder is always 0.
For example: 1,2,and 4 are the factors of 4.
Multiples
Multiples of a number are those numbers which are exactly divisible by the given number.
For example: The multiples of 4 are 4,8,12,16,20 etc.
Prime and Composite Numbers
A Prime Number is a number which has only two factors. The first factor is “1” and the second factor is the number itself.
A Composite Number is a number which has more than two factors.
LCM (Least Common Multiple)
LCM of two given numbers is the least number which is exactly divisible by each one of the given number.
Example: Find the LCM of 3 and 4
Given below is the list of multiples that 3 and 4 have:
The least common multiple between the two numbers is 12. Therefore, The LCM of 3 and 4 is 12.
HCF: Highest Common Factor
HCF of two or more given numbers is the highest number which exactly divides all the numbers.
Example: What is the HCF of 12 and 16?
Write down all the factors of the given number and check which is the highest common factor between the two given number:
Therefore, the HCF of 12 and 16 is 4.
Time and work
Important formulas
Work from Days:
If A can do a piece of work in n days, then A’s 1 day’s work = 
1 
. 
n 
 Days from Work:
If A’s 1 day’s work = 
1 
, 
then A can finish the work in n days. 
n 
 Ratio:
If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3 : 1.
Ratio of times taken by A and B to finish a work = 1 : 3.
Example :
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is : 


A’s 1 day’s work = 
1 
; 
15 
B’s 1 day’s work = 
1 
; 
20 
(A + B)’s 1 day’s work = 

1 
+ 
1 

= 
7 
. 
15 
20 
60 
(A + B)’s 4 day’s work = 

7 
x 4 

= 
7 
. 
60 
15 
Therefore, Remaining work = 

1 – 
7 

= 
8 
. 
15 
15 
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