Relationship Between HCF & LCM


 
 
Concept Explanation
 

Relation Between H.C.F. and L.C.M.

HCF : HCF stand for Highest Common Factor.It is also known as Greatest Common Division (GCD). The HCF of two or more given numbers is the highest of their common factors.

LCM: LCM stand for Lowest Common Multiple.It is also known as Smallest or Least Common Multiple.The LCM of two or more given numbers is the lowest of their common multiples.

Relation between HCF and LCM:

Product of two numbers = Product of their HCF and LCM.

X x Y =  HCF (X , Y)  X  LCM (X ,Y).

Illustration1 : HCF of two numbers is 16 and their product is 6400.Find their LCM ?

Solution: Product of two numbers = HCF X LCM

6400 = 16 X LCM

LCM = left (frac{6400}{16} right )

LCM=400.

Illustration2: LCM of two numbers is 15 and their product is 7500.Find their HCF?

Solution: Product of two numbers = HCF X LCM

7500 = HCF X 15

HCF = left ( frac{7500}{15} right )

HCF = 500.

Illustration 3 : HCF and LCM of two numbers is 16 and 15 respectively. Find their Product ?

Solution: Product of two numbers = HCF X LCM

Product of two numbers = 16 X 15

Product of two numbers = 240.

Illustration 4 : HCF and LCM of two numbers is 14 and 20 respectively. If one of the number is 10 , Find the other  ?

Solution: Product of two numbers = HCF X LCM

10 X other number = 14 X 20

other number = left ( frac{14 times 20}{10} right )

other number = 14 X 2 =28.

 

Sample Questions
(More Questions for each concept available in Login)
Question : 1

LCM of two numbers is

Right Option : D
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Explanation
Question : 2

Column - I                                                                                                                         Column - II

(A) The L.C.M of two prime numbers 'a' and 'b' (a>b) is 161. The value of 3b - a is                      (p)  322

(B) H.C.F of 4 X 27 X 3125,                                                                                                            (q) 130 

       8 X 9 X 25 X 7 and 16 X 81 X 5 X 11 X 49 is

(C) If the H.C.F of two numbers (each greater than 13) be 13 and the L.C.M be 273,                         (r)  -2

        then the sum of numbers is

(D) The H.C.F of two numbers is 23 and the other two

factors of their L.C.M are 13 and 14. The larger of the two number is                                             (s)  180

Choose the correct option:

Right Option : C
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Question : 3

Match the following.

Column AColumn B
I.  Smallest prime number is(i)  odd
II.  Number whose general form is 2n + 1, is(ii)  one
III.  HCF of two or more prime numbers is(iii) even
IV. A number which has no multiplicative inverse, is(iv)  zero

 

Right Option : C
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Explanation
 
 
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