hey dear i have doubt in word problems of this chapter real numbers
i have to know hole concept of HCF and LCM which is used in word problem.
hey dear i have doubt in word problems of this chapter real numbers
i have to know hole concept of HCF and LCM which is used in word problem.
It is very easy if we know the meaning of LCM and HCF.
Least Common Multiple, also called LCM is that smallest number which is completely divisible by a given set of numbers. For example, 30 is completely divisible by 5, 10 & 15 and hence is the LCM of 5,10 & 15. There is no number less than 30 that can boast the same.
So, whenever you are required to find a number that is divisible by more than one number, you have to find LCM.
Highest Common Factor, also called HCF, is that highest number that completely divides a given set of number. For example, 25 divides 50, 75, 100, 125, 725, 950. Since there is NO number greater than 25 that divides the given set of numbers, we call 25 as the Highest Common Factor or HCF.
So, whenever you are required to find a number that completely divides more than one number, you have to find HCF.
Coming to illustrative examples :
LCM
Three traffic signals change from Red to Green in 10, 15 & 20 seconds respectively. After how much time will all three signals together become Green ?
The three traffic signals will change from Red to Green as follows ( in seconds ):
First : 10,20,30,40,50,60,70,80 …..
Second : 15,30,45,60,75,90 …
Third : 20,40,60,80 …
It is clear the three signals will flash Green together after 60 seconds. Now , this 60 is completely divisible by 10, 15 & 20 and LCM(10, 15 , 20) is 60, hence the problem was of finding LCM.
Highest Common Factor(HCF)
Highest Common Factor(HCF) of two or more numbers is the greatest number which divides each of them exactly.
Greatest Common Measure(GCM) and Greatest Common Divisor(GCD) are the other terms used to refer HCF.
Example : HCF of 60 and 75 = 15 because 15 is the highest number which divides both 60 and 75 exactly.
One small example:
- When you are looking for a no that DIVIDES the no, then you have to find HCF.
- When you are looking for a no that is DIVISIBLE, then you have to find LCM.
It is very easy if we know the meaning of LCM and HCF.
Least Common Multiple, also called LCM is that smallest number which is completely divisible by a given set of numbers. For example, 30 is completely divisible by 5, 10 & 15 and hence is the LCM of 5,10 & 15. There is no number less than 30 that can boast the same.
So, whenever you are required to find a number that is divisible by more than one number, you have to find LCM.
Highest Common Factor, also called HCF, is that highest number that completely divides a given set of number. For example, 25 divides 50, 75, 100, 125, 725, 950. Since there is NO number greater than 25 that divides the given set of numbers, we call 25 as the Highest Common Factor or HCF.
So, whenever you are required to find a number that completely divides more than one number, you have to find HCF.
Coming to illustrative examples :
LCM
Three traffic signals change from Red to Green in 10, 15 & 20 seconds respectively. After how much time will all three signals together become Green ?
The three traffic signals will change from Red to Green as follows ( in seconds ):
First : 10,20,30,40,50,60,70,80 …..
Second : 15,30,45,60,75,90 …
Third : 20,40,60,80 …
It is clear the three signals will flash Green together after 60 seconds. Now , this 60 is completely divisible by 10, 15 & 20 and LCM(10, 15 , 20) is 60, hence the problem was of finding LCM.
Highest Common Factor(HCF)
Highest Common Factor(HCF) of two or more numbers is the greatest number which divides each of them exactly.
Greatest Common Measure(GCM) and Greatest Common Divisor(GCD) are the other terms used to refer HCF.
Example : HCF of 60 and 75 = 15 because 15 is the highest number which divides both 60 and 75 exactly.
One small example:
- When you are looking for a no that DIVIDES the no, then you have to find HCF.
- When you are looking for a no that is DIVISIBLE, then you have to find LCM.
