Relation Betweeen H.C.F and L.C.M:
Case(i) Product of two
numbers = Product of their H.C.F. and L.C.M.
Case(ii) There are n numbers. If the
HCF of each pair is x and the LCM of all the n numbers is y, then the product
of n numbers is given by or Product of ‘n’ numbers = (HCF of each
pair)n-1 × (LCM of n numbers).
Find the numbers:
1) The LCM of two numbers is 64699,
their GCM is 97 and one of the numbers is 2231. Find the other.
Solution:
Product of two numbers = Product of
their H.C.F and L.C.M
Given Data:
L.C.M = 64699 ; H.C.F = 97.
Let the number be : A = 2231.
Other number be : B =?
We know,
A× B = H.C.F × L.C.M
2231 × B = 97 × 64699
B = (97 × 64699) / 2231 = 2813.
Therefore,the
other number B = 2813.
2) The L.C.M of two numbers is 2079,
and their H.C.F is 27.If one of the number is 189 then find other number?
Solution:
Given Data
: L.C.M = 2079 ; H.C.F = 27.
Let one
number be A = 189;
The other
number be B =?
We know, A×
B = H.C.F × L.C.M
189 × B = 27 × 2079
B = (27 × 2079) / 189 = 297.
Therefore, the other number B = 297.
3) The ratio of the two numbers is
5:6. The L.C.M of two numbers is 480.Find out their H.C.F?
Solution:
Given: The
ratio of the two numbers = 5:6 ; L.C.M = 480.
Assume the
number be ‘x’, then the two numbers are = 5x and 6x.
We need to
find out H.C.F of two numbers : H.C.F(5x ,6x) = x.
Factors of 5x
= x ,5 ,
Factors of
6x = x, 6.
Therefore,
H.C.F( 5x,6x) = x.
We know, Product
of two numbers = Product of their H.C.F and L.C.M.
So,
(5x) × (6x) = x × 480
x = 16 .
Therefore, H.C.F
= 16.
4) There are 4 numbers. The HCF of
each pair is 3 and the LCM of all the 4 numbers is 116. What is the product of
4 numbers?
Solution:
Given : H.C.F of each pair =3 ; L.C.M
of 4 numbers = 116 ; n = 4.
We Know;
Product of ‘n’ numbers = (HCF of each pair)n-1 × (LCM of
n numbers).
Product of 4 numbers = (H.C.F of 2
pairs)4-1 × ( L.C.M of 4
numbers)
Product of 4 numbers = ( 3 ) 3 × 116
= 27 × 116 = 3132.
Therefore, Product of 4 numbers = 3132.
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