Product of the numbers = H.C.F . x L.C.M . This reaction holds for
Answers
Answer:
there is an interesting co-relation between H.C.F and L.C.M. of two numbers. The product of the H.C.F. and L.C.M. of any two numbers is always equal to the product of those two numbers. However the same is not applicable to three or more numbers.
☆Answer ☆
Why is the product of the LCM and HCF of two numbers that are equal to their products? What is its proof?
Let the two numbers be x and y.
Let LCM of x,y = L , HCF of x,y = H
now,
x = n*H & y = m*H for some n,m such that n & m are co-primes.
also L = n*m*H as n,m are co-primes.
H*L = n*H*m*H=x*y
If two numbers are 156 and 258, how can you show that the product of these two numbers is equal to the product of their LCM and HCF?
The product of two numbers is 2286. If their HCF is 9, what is their LCM?
How do we prove that the product of two natural numbers equals the product of their GCD and lCM?
What is the product of LCM and HCF?
The product of 2 numbers is 500, their LCM is 500. What is HCF?
Let xyzz and xyyz are two numbers
So, their HCF = xyz
And their LCM = xyyzz
So when we multiply the HCF and LCM we will get xxyyyzzz and also when we multiply the two numbers xyzz and xyyz ,then we will get xxyyyzzz so,both the product are equal so we can say that -
Product of two numbers= HCF×LCM
(Note- this formula can only be implemented on two numbers not on three or four …… numbers)
The HCF by definition contains all the common factors of two numbers, where as the LCM contains all the factors of the two numbers irrespective of common or un common. So the product of the two automatically contain all the factors common in double and non commons in single constituting the individual numbers in conglomerate for the proof of their product.
this is simple MATHS
If the product of two numbers is 2,028, and their HCF is 13, what are the numbers? What is the best way to explain this?
Before answering the question let us first see some pre requisites
What do we mean by HCF?
HCF stands for Highest Common Factor, which means that, if you are finding the HCF of two numbers, you are finding the highest(largest) number which is a factor of both the numbers. Since it is a factor of both the numbers we call it Common factor.
Now what do you mean by factor?
Factors are the numbers we multiply together to get another number.
By finding HCF of two numbers, we basically find the largest n...
The product of two numbers is 2286. If their HCF is 9, what is their LCM?
The product of highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of two numbers is equal to the product of two numbers.
Thus, 9 x LCM = 2286
LCM = 2286 / 9
LCM = 254
For any more questions of such type you can visit Relationship between H.C.F. and L.C.M. | Highest common Factor | Solved Examples [ http://www.math-only-math.com/relationship-between-hcf-and-lcm.html ]
The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. What are the numbers?
The product of LCM and HCF of two numbers is always equal to the product of the numbers
Let one number =x
Second number = x+2
Hence x*(x+2)=24
Or x^2+2x-24=0
I.e. (x+6)(x-4)=0
Now either x+6=0 i.e. x=-6
or x-4=0 i.e. x=4
Since the numbers are positive
Hence one numbers=x
And the second number=x+2=4+2= 6
4. and 4+2i.e. 6
4 and 6
How do we prove that the product of two natural numbers equals the product of their GCD and lCM?
The simplest way to prove
gcd(a,b)⋅lcm[a,b]=|ab|…(⋆)
is to use the Fundamental Theorem of Arithmetic, which states that every positive integer greater than 1 can be uniquely expressed as product of primes. Two representations are considered the same if one representation may be obtained from the other by permuting the prime factors, so all that counts for uniqueness is the number of occurrences of p in the factorization, for each prime p .
Recall that both gcd and lcm of any set of more than one non-zero integers are defined to be positive integers. This explains the the pres
The product of two numbers is 448 and their LCM is 112. What is the HCF?
Product of the 2 numbers = HC F ×LCM of the 2 numbers
448=112×X
X=448/112 =4
X = HCF is 4
The HCF of two numbers is 12 and the LCM is 72. What is the product of two numbers?
Let us take two numbers. 15 &35 . Let us determine the HCF & LCM.
15=3*5
35=5*7
HCF =5
LCM =3*5*7
HCF × LCM=(5) × (3*5*7)=(5*3)× (5*7)=15*35
The above shows that the product of HCF & LCM is equal to the Product of two numbers.