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How to slove hcf and lcm ,properties ,questions,formulas , tips and tricks of hcf and lcm ,short tricks with example

How to slove hcf and lcm ,formulas , tips and tricks of hcf and lcm ,short tricks with example. Hcf and lcm

How to slove hcf and lcm ,formulas , tips and tricks of hcf and lcm ,short tricks with example

Hcf and lcm


1. What is hcf ?                                  Hcf of any given set of number is the gratest factor comman to them.
Full form of hcf= highest comman factor or gratest comman factor .

2. What is lcm?                             
Lcm of the two or more numbers is the smallest number which is comman multiply of the given number.

Full form of lcm= lowest comman muntiply or smallest comman muntiply.
                                   

3. Concept of factor and multiple or concept of hcf and lcm.
When two or more numbers are multiplied together to give a product , each is called a factor of the product.
The product of two or more numbers is said to be a multiple of each of those numbers e.g.,
4*5=20 ,
Here ,4 and 5 are factors of 20 and 20 is a multiple of both 4 and 5.

4. Hcf (higest comman factor)

Hcf of two or more numbers is the greatest number which divides each of them exactly.
E.g.,, 6 is the hcf of 12 and 18 as there is no number to greater than 6 that divides both 12 and 13 . Hcf is also known as GCD and GCM which mean greatest comman divisor and greatest comman measure.

5.LCM (least comman multiple)

Lcm of two or more given numbers is the least number to be exactly divisible by each other of them 
E.g.,,, we can obtian lcm of 4 and 12 as follows.
Multiple of 4 =4,8,12,16.......
Multiple of 12=12,24,36.............
And comman muntiple of 4and 12 = 12,24,36,........

..,,lcm of 4 and 12 is 12 
Lcm is also known as least comman divident.

Important formule..,,

* hcf ×lcm = one number × another number.

*lcm of fraction= lcm of numertor/hcf of denometor

*hcf of fraction = hcf of numentor / lcm of denometor.

Question 1. The lcm of two numbers is 2079 and there hcf is 27. If the first number is 189 find the second number?

Solution,..,,  hcf   × lcm = one number  × another number.

27×2079=189× another number 
27×2079/189= another number

Another number is 297.

Question 2. Find the lcm and hcf of 25/6 and 15/4.

Solution 2. Lcm of 25/6 and 15/4 = lcm of (25, 15) / lcm of (6,4)=75/2

Hcf of 25/6  and 15/4 = hcf of (25,15)/ lcm of (6,4)= 5/12 

Question 3. Find the lcm of 0.6,9.6, and 0.12?

Solution 3. The given number are equivalent to 0.60, 9.6  and 0.12 now , and now we have to find the lcm of 60 ,960 nad 12 .
And lcm of 60 , 12 , 960 , is 960 
So requeired lcm is 9.60.

Question 4. Find the largest number that will divide 260, 720,and 145 leaving 7 as remainder in each case ?

Solution4.. Requerd number = HCF of (260-7),(720-7),(145-7)

= hcf of 253 ,713, and 138=23.

Question 5. The product of two relatively prime number is 143, find the HCF?
Solution.. Two relatively prime number are exactly divisible by 1 only .
Requried hcf =1


Target excerise with solve.

Question 1. How many numbers between 400 and 500 are exactly divisble by 12,15,20?
                
Solution 1. Lcm of 12 ,15,20,=60
Number 60 is divisible by each of 12 ,15,and 20and evry muntiple of 60 will be also divisible by 12,15,20.
120,180,240,300,360,420,480,540, and two numbers 420,480 lies betwwen 400 and 500. .

Question 2. The number betwwen 200 and 300 ,which when divided by 6,8,9 leaves remainder in each case  are , 

Solution2. Lcm of 6,8,9 =72 
Requreid number =( multiple of 72+8)which lies betwwen 200 and 300.
(72×3+8,72×4+8)=(224,396)


Question3.the HCF and lcm of two numbers are 21 and 4641 respectively .if one of the numbers lies between 200 and 300 ,the two numbers  are ?

Solution 3. Since , the hcf of two numbers is 21, hence let the number be 21x. × 21y respectively . We know that , product of two numbers = hcf x lcm 

21x × 21y =21×4641
Xy= 221=(13×17)

Because x and y are co prime numbers therfore the numbers are (21×13,21×17)(273,357).

Question  ,,solve it..

Question 1 . Find the gratest number which can be divide 284,698 and 1618 leaving same reaminder in eeach case.

Answer 1.  46 .

Question 2. Find the largest number which divides 62,132, and 237 to leave the same reaminder in each case .

Answer. 35 .

Question 3.  Find the largest number of four digits exactly divisible by 12,15,18,nad 27.

Answer . 9720.

Question 4. Find the smallest number of five digits exactly divides by 16, 24 ,36, and 54 ?

Answer 4. 10368 .

Question 5. The differce of two numbers is 1/9 of there sum . And there sum is 45 . Find the lcm.

Answer 5. 100 .

Question with hints ,...

Question 1 . Five bells first began to toll together and then at intervals of 3 and  5 or 10 s . Find after what interval they will aganin toll togeather .how many tolls does tehy toll togeather in one houre.

Answer. 1.  Requried time interval = lcm of 3,5,7,8  and 10 = 840 s =14 minuties 

Number of time they toll toll togeather inone hour 
60/14= 4 times 
(ignoring the fraction part).

Propety of factor and muntiple or hcf and lcm.


Propety of hcf = hcf of two numbers or more numbers is the greatest numbers which divides each of them exactly .


Property of lcm = 
Eg. We can obtain lcm of 4and 120 as follows.
Muntiple of 4=,4 ,8 ,12, 16, ,,,,....
Muntiple of 12= 12, 24 ,36 ,48, ......
Comman multiple of 4and 12=12, 24 ,36 ,.....

Lcm of 4 ,and 12 is 12 .

Question 1. Find the smallest whole number which is exactly divisble by 1-

Question 2 ,. The hcf of 9/10 , 12/25 , 18/35 , and 21/40 is ? 

Answer.  Hcf of 9/10 , 12 / 25 , 18/35 , 21/40 

= hcf of (9,12 18,21) / lcm of (10, 25 ,35 ,40 )  is equal to 3/1400 

Henc, the answer is 3/1400.

Thankss..,.,.,,.,.


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Hcf and lcm 

1. Question12. The lcm of 2/3,3/5,4/7,9/13.

Answer 12. Lcm of 2/3, 3/5, 4/7,9/13=lcm of (2,3,4,9)/hcf of (3,5,,7,13)=36/1 
And the answer is 36.

Question13. A general can draw up his soldiers in the rows of 10,15, or 18 soldiers and he can also draw them up in the form of a solid square . Find the least number of soldiers with the gernal.

Question 14. Find the greatest possible length of the planls ,if three pieces of timber 42m , 49m , and 63m, long have to be divided into planks of the same length.

Question15. What is the least number by which 2352, is to be multiplied to make it a perfect square.

Question16. An officer was appointed on a maximum daily wages on a contrast money 4956, but on  being absent for some days , he was paid 3894. For how amny days was he absent.

Question17. What is the least number which when incread by 9 , is divisible by each other one 24, 32, 36, amd 54?

Qiestion 18. Find the least number whoch when divided by 16 ,18,20, leaves a reminder 4 in each case , but is compltely divisble by 7. 

Question19.the least number which should be added to 2497. So that the sum is exactly divisble by 5,6,4, nad 3 is .

Question 20 . The smallest fraction which is exactly divisble by each other of 6/7 , 5/14, 10/21. Is

Question 21. Five ablls beings to toll togeather at intervals of 9s , 6, 8, 10,8,s . How many times will they toll togeather in the span of one hour (excluding the toll at the start).

Question22. Monica ,veronica and rachat beigns to jog around a circular stadium .they complete their to jog around a 42 s, 56 , 63, repectivelg .after how many seconds they be together at the startingg point.











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