HCF and LCM OF NUMBERS | hcf and lcm- open2study

LCM ADN HCF OF NUMBERS


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IMPORTANT FACTS AND FORMULAE
what is factor :  a number is said to be a factor of another number it divides the other number exactly.

for example:- 2 and 4 is a factor of 8

what is common factor : A common Factor of two or more numbers is a number that divides each of them exactly. 

for example:- 3 is a common factor of 9, 15, 21 
what is Highest Common Factor (HCF) : HCF of two or more numbers is the greatest factor which divides each of them exactly. 

for example:- 12 is the HCF of 24 and 36.


how to find  HCF

 

Prime Factorization:- First of all the numbers are broken into prime factors and then all the common factors of all the numbers are multiplied to get the HCF.

1. Find the HCF of 42, 70 and 126
Ans
          

 Division Method – The greater is divided by the smaller number, then the divisor is divided by the remainder, then the remainder is divided by the next remainder and the process continues until no remainder is left. The last divisor is the required HCF.

In case of Calculation of HCF of more than two numbers, first of all HCF of any two numbers is calculated and then we find the HCF of this HCF and the third number and so on. The last HCF will be the required HCF
2. Find the HCF of 42, 70 and 84
                   

 14 is the HCF of 42 and 70
Now,
                   

 The required HCF=14
HCF of Decimals: Firstly make ( if necessary ) the same number of decimal places in all the given numbers, then their HCF is found as if they were integers and then as many decimal places are marked off as there are in each of the numbers.

3. Find HCF of 17.40, 0.45 and 15
Ans: The given numbers are equivalent to 17.40, 0.45 and 15.00.

 HCF of 1740, 45 and 1500 is 15.
Required HCF =0.15

HCF of Fractions: The HCF of two or more fractions is the highest fraction which is exactly divisible by each of the fraction. First of all the given fraction are expressed in their lowest terms.

 Then HCF= HCF of numerators / LCM of denominators
 
what is Multiple: A multiple of a number is a number which is exactly divisible by the number.
what is Common Multiple: A common multiple of two or more numbers is a number which is exactly divisible by each of them.


 what is Lcm (Least Common Multiple ): The LCM of two or more given numbers is the least number which is exactly divisible by each of them.

1 
Prime Factorization Method:- In this method, the given numbers are resolved into their prime factors and then the product of the highest power of all the factors that occur in the given numbers are found. This product is the LCM.
4. Find the LCM of 8, 12 and 15
Ans:
          
Division by Prime Factor Method: Numbers are written down in a line and are separated by commas. Then they are divided by any prime numbers which will exactly divide at least two of them. Set down the quotients and the undivided numbers in a line below the first. The product of all the divisors and the numbers in the least line is the required LCM.

5. Find the LCM of 8 ,12 and 15
          

6. Find the LCM of 0.6, 9.6 and 0.36.
Ans : The given numbers are equivalent to 0.60, 9.60 and 0.36
Now, LCM of 60, 960 and 36 is 2880
Required LCM = 28.80
7. the LCM of two numbers is 60 and their HCF is 3. If one of the numbers is 15, Find the other number.