lcm and gcd questions and answers with simple tricks.

GCD ( HCF )and LCM questions and answers :
GCD ( HCF ) and LCM
GCD stands for greatest common divisors.
Or HCF stands for highest common factor.
LCM stand for Lowest Common Multiple.
  • LCM it a small number that can be divided completely by the other given numbers.
  • GCD it is the largest number which can divided the given numbers.
  • GCD is always smaller or equal to a smaller number.
  • LCM is always equal to or larger than a large number.
  • LCM of fraction :
  • LCM = LCM of numerators / GCD of denominators.
  • GCD of fraction :
  • GCD = GCD of numerators / LCM of denominators.
  • LCM of prime numbers is theirs multiplication.
  • GCD of prime numbers is always one.
  • Relation between LCM and GCD in two numbers is :
  • First number × second number = LCM × GCD
Lowest Common Multiple ( LCM ) :
  • LCM it a small number that can be divided completely by the other given numbers.
Methods of finding LCM :
List Method :
Question: Find the LCM 
1) 5 , 8.            2) 4, 6.           3) 3, 7
1) 4, 6
Ans. :
Multiplication table of 15 : 15, 30, 45, 60, 75, 90,105, .......
Multiplication table of 18 : 18, 36, 54, 72,90,108, .....
Common multiples of 15 and 18 : 90,.....
The smallest of these numbers 90.
Therefore, LCM 40.
Divisibility Method :
3 | 15 | 18
5 | 05 | 06
6 | 01 | 06
   | 01 | 01
   
Multiplication of 3 × 5 × 6 = 90.
Therefore, LCM 90.
2) 4, 6
Ans.
List method :
Multiplication table of 4 : 4, 8, 12, 16, 20, 24, .....
Multiplication table of 6 : 6, 12, 18, 24, 30, 36, .....
Common multiples of 4 and 6 : 12, 24, ....
The smallest of these numbers 12.
Therefore, LCM 12.
Divisibility Method :
2|  4 |  6
2|  2 |  3  
3|  1 |  1
Multiplication of 2 × 2 × 3 = 12
Therefore, LCM 12.
3) 3, 7.
Ans. : LCM of prime numbers is theirs multiplication.
Therefore, 3 × 7 = 21.

Greatest common divisors ( GCD ) :
  • GCD it is the largest number which can divided the given numbers.
  • GCD is always smaller or equal to a smaller number.
Methods of finding GCD :
List method :
Example :
1) Find the GCD of 6 and 8.
Ans. :
Divisors of 6 : 1, 2, 3, 6.
Divisors of 8 : 1, 2, 4, 8.
Of the common divisors 1 and 2, 2 is the biggest.
Therefore, GCD of 6 and 8 is 2.
Divisibility method :
2 | 6 | 8
   | 3 | 4
Multiplication of Common divisor is 2.
Therefore, GCD of 6 and 8 is 2.
2) Find the GCD of 20 and 30.
Ans. :
Divisors of 20 : 1, 2, 4, 5, 10, 20.
Divisors of 10 : 1, 2, 5, 10.
Of the common divisors 1, 2, 5 and 10, 10 is the biggest.
Therefore, the GCD of 20 and 30 is 10.
Divisibility Method :
2 | 20 | 30
5 | 10 | 15
   | 02 | 03
Multiplication of  Common divisors 2 × 5 = 10.
Therefore, GCD of 20 and 30 is 10.
3) Find the GCD of 5 and 11.
Ans. :
GCD of prime numbers is always one.
Therefore GCD of 5 and 11 is One.

LCM of fraction :
LCM = LCM of numerator / GCD of denominator.
Example :
Q. Find the LCM
1) 2/3, 4/9.              2) 10/12, 5/6.
1) 2/3, 4/9.
Ans. :
LCM of numerator values : 2, 4.
By divisibility method :
2 | 2 | 4
2 | 1 | 2
   | 1 | 1
Multiplication of 2 × 2 = 4.
Therefore, LCM of 2 and 4 is  4.
GCD of denominator values : 3, 9.
By divisibility method :
3 | 3 | 9
   | 1 | 3
Multiplication of Common divisor is 3
Therefore, GCD of 3 and 9 is 3.
Now, LCM of 2/3 and 4/9 is 4/3.
2) 10/12, 5/6.
Ans. :
LCM of numerator values : 10, 5
By divisibility method :
2 | 10 | 5
5 | 05 | 5
   | 01 | 1
Multiplication of 2 × 5 = 10.
Therefore, LCM of 10 and 5 is 10.
GCD of denominator values : 12, 6
By divisibility method :
2 | 12 | 6
3 | 06 | 3
   | 02 | 1
Multiplication of Common divisor is 2 × 3 =6
Therefore, GCD of 12 and 6 is 6.
Now, LCM of 10/12 and 5/6 is 10/6.

GCD of fraction :
  • GCD = GCD of numerators / LCM of denominators.
Example :
Que To Find the GCD
1) 2/3, 4/9.                 2) 9/10, 12/16
1)2/3, 4/9
Ans. :
GCD of numerator values : 2, 4
By divisibility method :
2 | 2 | 4
   | 1 | 2
Multiplication of Common divisor is 2.
Therefore, GCD of 2 and 4 is 2.
LCM of denominator values : 3, 9
By divisibility method :
3 | 3 | 9
3 | 1 | 3
   | 1 | 1
Multiplication of 3 × 3 is 9.
Therefore, LCM of 3 and 9 is 9.
Now, GCD of 2/3 and 4/9 is 2/9.
2) 9/10, 12/16
Ans. :
GCD of numerator values : 9, 12
By divisibility method :
3 | 9 | 12
   | 3 | 04
Multiplication of Common divisor is 3.
Therefore, GCD of 9 and 12 is 3.
LCM of denominator values : 10, 16
By divisibility method :
2 | 10 | 16
2 | 05 | 08
2 | 05 | 04
2 | 05 | 02
5 | 05 | 01
   | 01 | 01
Multiplication of 2 × 2 × 2 × 2 × 5 = 80.
Therefore, LCM of 10 and 16 is 80.
Now, GCD of 9/10 and 12/16 is 3/ 80

  • Relation between LCM and GCD in two numbers is :
  • First number × second number = LCM × GCD
 Example:
1) The LCM of 10 and 15 is 30, so what is the GCD?
Ans. :
First number × Second number = LCM × GCD
10 × 15 = 30 × GCD
( 10 × 15 ) / 30 = GCD
Therefore, GCD = 5.
2) The GCD of 15 and 18 is 3, so what is the LCM?
Ans. :
First number × Second number = LCM × GCD
15 × 18 = LCM × 3
( 15 × 18 ) / 3 = LCM
Therefore, LCM = 90.
3) The two numbers are 4x and 10x, their GCD is 12 and LCM is 120, so x=?
Ans. :
First number × Second number = LCM × GCD
4x × 10x = 12 × 120
40 ( x × x ) = 12 × 120
x × x = ( 12 × 120 ) / 40
x  × x = 36
x × x = 6 × 6
Therefore, x = 6.

Related Links :

 1. Divisibility Rules :

 2. Number System math :

 3. Ratio and Proportion :

 4. Percentage tricks and shortcuts :

 5. Profit and loss math tricks :

 6. Average problems tricks and shortcuts :

 7. lcm and gcd questions and answers :

Comments

Post a Comment

Popular posts from this blog

Series Order tricks, shortcuts and examples.

Image
Series Order tricks : A category of three, four or some numbers is given in the competitive examination. There is a mutual relationship among these numbers. The same relationship has to be understand and the same basis is to be increased further. Examples : 1) What will be the next number in the following series. 3, 10, 31, 94, ----- Ans. : Each terms is increasing by : ( n × 3 ) + 1. Therefore, ( 3 × 3 ) + 1 = 10 ( 10 × 3 ) + 1 = 31 ( 31 × 3 ) + 1 = 94 ( 94 × 3 ) + 1 = 283 Therefore, next number : 283. 2) Find the next order in the category. 1, 4, 9, 16, ---- Ans. : Each term is a squares of consecutive numbers. therefore, 5 × 5 = 25. therefore, next number = 25. Examples : Q. What will be the next number in the following series .  1) 3, 6, 10, 15, 21, ---- Ans. : The difference in each term is increasing in the form of consecutive numbers. that is 3 + 3 = 6. 06 + 4 = 10. 10 + 5 = 15. 15 + 6 = 21. 21 + 7 = 28. There
Read more

Quartile Definition, formulas, First Quartile, Third Quartile, How to calculate the Quartile.

Image
Quartiles : Quartile Definition : " All data divided four equal parts is known as Quartile. " It is clear that the items which divided the data into four equal parts lie at the quarter, half and three quarters, of the way down the arrangement. Quartile denoted by Q1 means first quartile, Q2 means second quartile, Q3 means third quartile respectively. Clearly the second quartile is the Median item. Mean         Median          Mode Quartile Formulas : For Individual items and Discrete Distribution : 1) First Quartile = Q1 = Size of [ ( N + 1 ) / 4 ]th item. 2) Third Quartile = Q3 =  Size of 3 × [ ( N + 1 ) / 4 ]th item For Continues Distribution : 1)  First Quartile = Q1 = Size of [ N / 4 ]th item. 2) Third Quartile= Q3 =Size of 3 × [ N / 4 ] th item Quartiles Examples : Computation of Quartiles for Individual Data : 1) Calculate the first, second and third quartile from the following values weights in kg of a group of students. 50, 51
Read more

Decile : Decile Definition, How to calculate Decile, Decile Formulas.

Image
Decile : Decile Definition : " All data divided Ten equal parts is known as Decile. " It is clear that the items which divided the data into ten equal parts lie at the D1, D2, ...., D10 of the way down the arrangement. Decile denoted by D1 means first decile, D2 means second decile, and so on D10 means tenth decile respectively.               Mean          Median         Quartiles Decile Formulas : For Individual items and Discrete Distribution : 1) First Decile = D1 = Size of [ ( N + 1 ) / 10 ]th item. 2) Second Decile = D2 =  Size of 2 × [ ( N + 1 ) / 10 ]th item. 3) Third Decile = D3 = Size of 3 × [ ( N + 1 ) / 10 ] th item. and so on, 10) Tenth Decile = D10 = Size of  ( N + 1 ) th item. For Continues Distribution : 1) First Decile = D1 = Size of [ N / 10 ]th item. 2) Second Decile = D2 = Size of 2 × [ N / 10] th item and so on, 10) Tenth Decile = D10 = Size N th item. Deciles Examples : Computation of Dec
Read more