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LCM and HCF

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Least Common Multiple and Highest Common Factor

Introduction:

* Factor and Multiple: If the first number of two numbers completely divided, the first number of the second number is Factor And the second number is called Multiple of the first number.

Example: Number 3 is a factor of 24, whereas number 24 is the number of number 3.


 

* Shortest Complexity (L.C.M.): The small number that is divided completely from each given number, the given numbers are called the shortest metabolism.

 

* Shortest Closure Removal: The following two methods to determine L.C.M are: –

 

(1) [Prime Factorization Method]

Verb method –
(i)
First of all, express each of the given numbers as a prime factor.
(ii)
Select all of these dividend factors with the biggest cause. Take, which is included in the multiplication of any number of them.
(iii)
Now selected by multiplying the given multiplier lines selected LC.M. Find out

 

Example: What is L.C.M. of 18, 28, 108 and 105?
Here,
18 = 2 × 3 × 3 = 2 × 32
28 = 2 × 2 × 7 = 22 × 7
108 = 2 × 2 × 3 × 3 × 3 = 22 × 3 3
And 105 = 3 × 5 × 7
Distressed L.C.M. = 22 × 33 × 5 × 7 = 4 × 27 × 5 × 7 = 3780 Ans.
Here, the biggest deficit of 2 and 3 is 22 and 33 respectively, and the second prime factor is 5 and 7 respectively.

 

(2) [Division Method]

verb method –
(i)
put the given numbers in a row and divide the lowest number of prime numbers 2 3 5 7 11 etc., which will be completed in at least two of these given numbers. Run away

(ii) After that, the gaps which are received and those numbers which can not be distributed in the given numbers, fall in the second row.

(iii) The first line of action can be done in the second, third rows with the smallest number, it may be possible to repeat an action.

(iv) Multiply all the divisors and the last row numbers and get the received L. C. M.

 

Example: What is L.C.M. of 36, 60, 84 and 90?
Solution:

Therefore, the specified L.C.M. = 2 × 2 × 3 × 3 × 5 × 7 = 1260 Ans.

 

L.C.M. of Decimals

verb method –
L.C.M. of given decimal numbers To find their corresponding full number of LC.M. Remove and get the decimal number inserted after the number in the LCM by number, as the number of decimal points in the decimal is decimal to the right after the decimal.

Example: What is L.C.M. of 2.4, 0.36, 0.045?
Solution:

L.C.M. of compatible full number = 3 × 3 × 4 × 2 × 5 = 360
So, nowadays L.C.M. = 36.0 = 36 Ans.

Note: Here number 2 is the number of digits after decimal in decimal number. That is why L.C.M. of full numbers A decimal is set in 360 after the ‘0’ from the right side.

 

L.C.M. of Fractions


Formula:

 

Minimal wings of exposure and exponent (L.C.M. of Power and Base)

TYPE-1
Trick – If the base number of the given numbers is same and the power is uneven, then their LCM is the maximum power number

 

Example 1. 37   312   317 What will be the smallest endowment?
Solution: LC.M. = 317 Answer.

 

Example 2. 5-9   5-7   5-14 What will be the smallest endowment?
Solution: 5-7 Answer. [∵ -7 > -14]

 

TYPE – 2
TRICK – If the given numbers are both ambient and density, then their L.C.M. Factor is known by method.

 

 

Highest Common Factor: The greatest converter of two or more numbers (H.C.F.) is a large number that divides each of them completely.

The method of finding the greatest convergent – The following two methods of removing the greatest particle are:

 

1. Prime Factorization Method
Action Method –
(i)
Express each of the given numbers as a prime factor.
(ii)
Find out the product of which the productivity is present in all numbers i.e., the most, the product of these numbers will be HCF.

 

Example: What will be the greatest consumer of 28 and 32?
Solution:
28 = 2 × 2 × 7 and
32 = 2 × 2 × 2 × 2 × 2
The given numbers 28 and 32 have the common factor 2 and 2, so the desired H.C.F = 2 × 2 = 4 Ans.

 

2. Continued Division Method
Action Method –
(i)
First of all given numbers, divide large numbers into small numbers.
(ii)
Then divide the remaining ones before the separator. That is, this is the second separator.
(iii)
If left then remaining part from this new balance into another separator.
(iv)
repeat this action until the remaining zero is received.
(v)
Thus, the lastest separator is given the H.C.F. Will happen.

 

Example: What will be the greatest exponent of 493 and 928?
Solution:

 

H.C.F. of three or more numbers Detection Method:

Action Method –
(i)
The first two numbers of H.C.F. Determine by continuously splitting method,
(ii)
Then this H.C.F and any remaining number of H.C.F. Find out.
(iii)
Perform this verb with all the given numbers.
(iv)
Lastly the H.C.F. You will get the same H.C.F. Will happen.

 

 

 

H.C.F. of Decimals

Action Method –

H.C.F. To find their corresponding full numbers, H.C.F. Remove and get H.C.F. Put the decimal after the number of points on the right side, as the number of maximum digits in decimal is numbered after the decimal point,

 

Example: What will be the greatest contributor to 1.5, 0.24 and 0.036?
Solution:
15 = 3 × 5
24 = 3 × 23
36 = 3 × 3 × 22
H.C.F = 3 of corresponding full
Therefore, the desired H.C.F = 0.003 Answer.

 

The greatest Fractions of fractions

Formula:

 

 

The greatest exponent of power and exponent (H.C.F. of Power and Base)

TYPE-1
TRICK – If the base of the given numbers is identical and the power is uneven, then their H.C.F. What is the minimum power number?

 

Example 1: What would be the greatest consumer of  28  210  215 ?
Solution: Expected H.C.F = 28

 

Example 2: 7-12  7-13  7-18 What would be the greatest consumer?
Solution: Expected H.C.F = 7-18 Answer. [∵ -18 < -12]

 

TYPE – 2
TRICK – If the given numbers are both ambient and density, then their H.C.F. Factor is known by method.

Example 1: 52   43 What will be the greatest consumer?
Solution: 52 = 1 × 52 and 43 = 1 × 43
Expected H.C.F = 1 Answer.

 

 Formula: First Number × Second Number = H.C.F × L.C.F

 

Example: The greatest common denominator of the two numbers and the smallest clusters are 12 and 396, respectively. If one of them is 36, what would be the second number?

 

Objective type Questions, Notes for Govt Exams, current affairs, general knowledge, hindi objective questions, English objective questions, Mathematics objective Questions, Reasoning Objective Questions, study material for IBPS, study material for banks, study material for SSC, study material for DSSSB, Aptitude objective type Questions, Solved Question papers, Notes, Study Material, general knowledge questions and answers, gk questions and answers, hindi questions and answers, English questions and answers , mathematics questions and answers, reasoning questions and answers, current affairs questions and answers, general knowledge questions and answers for competitive Exams, gk questions and answers for competitive Exams, hindi questions and answers for competitive Exams, English questions and answers for competitive Exams, Mathematics questions and answers for competitive Exams, reasoning questions and answers for competitive Exams, current affairs questions and answers for competitive Exams, Railway jobs, banking job, corporate jobs, government jobs, govt jobs, private jobs, CPO, PCS, RRB, CDS, UPSC,Notes, Online Tests, practice sets, questions and answers with explanation for competitive examination, entrance test, Railway, IBPS, SSC, DSSSB, PCS, Banking for hindi, english, mathematics, reasoning, gk, current affairs and many more.





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