How to do HCF and LCM
Answers
Here are the methods we can use to find the HCF and LCM of given numbers.
Prime factorisation method
Division method
Let us learn both the methods one by one.
Prime Factorisation for HCF
Take an example of finding the highest common factor of 144, 104 and 160.
Now let us write the prime factors of 144, 104 and 160.
144 = 2 × 2 × 2 × 2 × 3 × 3
104 = 2 × 2 × 2 × 13
160 = 2 × 2 × 2 × 2 × 2 × 5
The common factors of 144, 104 and 160 are 2 × 2 × 2 = 8
Therefore, HCF (144, 104, 160) = 8
Division method to find the HCF (Shortcut method)
Steps to find the HCF of any given numbers;
1) Larger number/ Smaller Number
2) The divisor of the above step / Remainder
3) The divisor of step 2 / remainder. Keep doing this step till R = 0(Zero).
4) The last step’s divisor will be HCF.
The above steps can also be used to find the HCF of more than 3 numbers.
Example: Find the HCF of 144 and 160 by division method.
Since 160>144, so the dividend will be 160 and the divisor will be 144.
By using the division method, we get:
HCF by Long division method
Hence, we can see here 16 is the highest number which divides 160 and 144.
Therefore, HCF (144, 160) = 16
LCM By Prime Factorisation
To calculate the LCM of two numbers 60 and 45. Out of other ways, one way to find the LCM of given numbers is as below:
List the prime factors of each number first.
60 = 2 × 2 x 3 × 5
45 = 3 × 3 × 5
Then multiply each factor the most number of times it occurs in any number.
If the same multiple occurs more than once in both the given numbers, then multiply the factor the most number of times it occurs.
The occurrence of Numbers in the above example:
2: two times
3: two times
5: one time
LCM = 2 × 2 x 3 × 3 × 5 = 180
LCM by Division Method
Let us see with the same example, which we used to find the LCM using prime factorisation.
Solve LCM of (60,45) by division method.
LCM by long division method
Therefore, LCM of 60 and 45 = 2 × 2 x 3 × 3 × 5 = 180
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The highest common factor is found by multiplying all the factors which appear in both lists: So the HCF of 60 and 72 is 2 × 2 × 3 which is 12. The lowest common multiple is found by multiplying all the factors which appear in either list: So the LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 which is 360.