Relationship Between HCF & LCM
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 =
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 =
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 =
other number = 14 X 2 =28.
Consider the following statements. (i) If L.C.M. of two numbers 6 and 8 is 24, then their H.C.F. is 2. (ii) First number X Second number = L.C.M X H.C.F Which of the above statement (s) is /are correct | |||
| Right Option : C | |||
| View Explanation |
Find LCM of two number when HCF and their product is 24 and 4032 respectively. | |||
| Right Option : D | |||
| View Explanation |
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 | |||
| View Explanation |
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