How to find Hcf and lcm using prime factorization

 The full types of H.C.F. what's more, L.C.M. are, Highest Common factor and Least Common Multiple, separately. The H.C.F. characterizes the best figure present between given at least two numbers, though L.C.M. characterizes the most un-number which is actually distinct by at least two numbers. H.C.F. is likewise called the best regular factor (GCF) and LCM is additionally called the Least Common Divisor. 

https://www.calculatorschool.com/Numbers/HCFandLCMCalculators.aspx

To discover H.C.F. also, L.C.M. we have two significant techniques which are the Prime factorization strategy and division technique. We have learned both the strategies in our previous classes. The easy route strategy to discover both H.C.F. also, L.C.M. is the division technique. Let us become familiar with the connection between HCF and LCM with the assistance of the equation here. Additionally, we will tackle a few issues dependent on these two ideas to see better. 


More is here: Learn Mathematics 


HCF and LCM Definition 


We realize that the variables of a number are precise divisors of that specific number. How about we continue to the most noteworthy basic factor (H.C.F.) and the most un-normal numerous (L.C.M.). 


HCF (Highest Common Factor) 


As the principles of arithmetic direct, the best normal divisor or the gcd of at least two positive numbers turns out to be the biggest positive whole number that isolates the numbers without leaving a leftover portion. For instance, take 8 and 12. The H.C.F. of 8 and 12 will be 4 on the grounds that the most elevated number that can separate both 8 and 12 is 4. 


LCM (Least Common Multiple) 

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In number-crunching, the most un-regular various or LCM of two numbers state an and b, is meant as LCM (a,b). Also, the LCM is the littlest or least certain number that is distinct by both an and b. For instance, let us take two positive whole numbers 4 and 6. 


Products of 4 are: 4,8,12,16,20,24… 


Products of 6 are: 6,12,18,24… . 


The basic products for 4 and 6 are 12,24,36,48, etc. The most un-basic different in that part would be 12. Let us currently attempt to discover the LCM of 24 and 15. 


LCM of 24 and 15 


LCM of 24 and 15 = 2 × 2 × 2 × 3 × 5 = 120 


LCM of Two Numbers 


Assume there are two numbers, 8 and 12, whose LCM we have to discover. Let us compose the products of these two numbers. 


8 = 16, 24, 32, 40, 48, 56, … 


12 = 24, 36, 48, 60, 72, 84,… 


You can see, the most un-regular various or the littlest basic difference of two numbers, 8 and 12 is 24. 


HCF and LCM Formula 


The recipe which includes both HCF and LCM is: 


Result of Two numbers = (HCF of the two numbers) x (LCM of the two numbers) 


State, An and B are the two numbers, at that point according to the equation; 


A x B = H.C.F.(A,B) x L.C.M.(A,B) 


We can likewise compose the above recipe regarding HCF and LCM, for example, 


H.C.F. of Two numbers = Product of Two numbers/L.C.M of two numbers 


and 


L.C.M of two numbers = Product of Two numbers/H.C.F. of Two numbers 


Related Links 


Hcf 


Lcm 


Properties Of Hcf And Lcm 


Connection Between Hcf And Lcm 


Lcm Of Two Numbers 

https://byjus.com/maths/hcf-and-lcm/

How to discover HCF and LCM? 


Here are the techniques we can use to discover the HCF and LCM of given numbers. 


Prime factorization strategy 


Division strategy 


Let us learn both the strategies individually. 


Prime Factorisation for HCF 


Take an illustration of finding the most elevated regular factor of 144, 104 and 160. 


Presently let us compose the prime components 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 regular elements of 144, 104 and 160 are 2 × 2 × 2 = 8 


Accordingly, HCF (144, 104, 160) = 8 


Division strategy to discover the HCF (Shortcut technique) 


Steps to discover the HCF of some random numbers; 


1) Larger number/Smaller Number 


2) The divisor of the above advance/Remainder 


3) The divisor of stage 2/leftover portion. Continue doing this progression till R = 0(Zero). 


4) The last advance's divisor will be HCF. 


The above advances can likewise be utilized to discover the HCF of multiple numbers. 


Model: Find the HCF of 144 and 160 by division strategy. 


Since 160>144, so the profit will be 160 and the divisor will be 144. 


By utilizing the division strategy, we get: 


HCF by Long division strategy 


Henceforth, we can see here 16 is the most elevated number which partitions 160 and 144. 


Hence, HCF (144, 160) = 16 


LCM By Prime Factorisation 


To ascertain the LCM of two numbers 60 and 45. Out of different ways, one approach to discover the LCM of given numbers is as beneath: 


Rundown the prime variables of each number first. 


60 = 2 × 2 x 3 × 5 


45 = 3 × 3 × 5 


At that point increase each factor extremely number occasions it happens in any number. 


On the off chance that a similar various happens more than once in both the given numbers, at that point increase the factor extremely number occasions it happens. 


The event of Numbers in the above model: 


2: two times 


3: two times 


5: once 


LCM = 2 × 2 x 3 × 3 × 5 = 180 


LCM by Division Method 


Let us see with a similar model, which we used to discover the LCM utilizing prime factorization. 


Fathom LCM of (60,45) by division technique. 


LCM by long division strategy 


Accordingly, LCM of 60 and 45 = 2 × 2 x 3 × 3 × 5 = 180 


At BYJU'S you can likewise learn, Prime Factorization Of Hcf And Lcm. 


HCF and LCM Questions 


Model: Find the Highest Common Factor of 25, 35 and 45. 


Arrangement: Given, three numbers as 25, 35 and 45. 


We know, 25 = 5 × 5 


35 = 5 × 7 


45 = 5 × 9 


From the above articulation, we can say 5 is the main normal factor for all three numbers. 


Thusly, 5 is the HCF of 25, 35, and 45. 


Model: Find the Least Common Multiple of 36 and 44. 


Arrangement: Given, two numbers 36 and 44. Let us discover the LCM, by division strategy. 


HCF and LCM QuestionsTherefore, LCM(36, 44) = 2 × 2 × 3 × 3 × 11 = 396

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