If the L.C.M. of x and y is z, their H.C.F. is Options: A . &nbspxyz B . &nbsp \(\frac{x+y}{z}\) C . &nbsp \(\frac{z}{xy}\) D . &nbsp \(\frac{xy}{z}\)

Answer: Option D Let x and y be two positive integers with their L.C.M. as z. We need to find their H.C.F. The product of two numbers is equal to the product of their L.C.M. and H.C.F. This can be expressed mathematically as: x*y = L.C.M. (x, y) * H.C.F. (x, y) Using the given information, we can write: x*y = z * H.C.F. (x, y) Therefore, the H.C.F. (x, y) is given by: H.C.F. (x, y) = (x*y)/z Hence, the answer is Option D, i.e., xy/z. Definitions: L.C.M. (Least Common Multiple): The smallest positive integer that is a multiple of two or more given numbers. H.C.F. (Highest Common Factor): The greatest positive integer that divides two or more given numbers without leaving a remainder. Formulas: Product of two numbers = L.C.M. of the two numbers * H.C.F. of the two numbers H.C.F. of two numbers = (Product of the two numbers) / (L.C.M. of the two numbers) In this question, we have used the second formula to derive the expression for the H.C.F. of x and y.

If the L.C.M. of x and y is z, their H.C.F. is

Question

If the L.C.M. of x and y is z, their H.C.F. is

Options:

A . xyz

B . \(\frac{x+y}{z}\)

C . \(\frac{z}{xy}\)

D . \(\frac{xy}{z}\)

Answer: Option D
Let x and y be two positive integers with their L.C.M. as z. We need to find their H.C.F.
The product of two numbers is equal to the product of their L.C.M. and H.C.F. This can be expressed mathematically as:
x*y = L.C.M. (x, y) * H.C.F. (x, y)
Using the given information, we can write:
x*y = z * H.C.F. (x, y)
Therefore, the H.C.F. (x, y) is given by:
H.C.F. (x, y) = (x*y)/z
Hence, the answer is Option D, i.e., xy/z.
Definitions:

L.C.M. (Least Common Multiple): The smallest positive integer that is a multiple of two or more given numbers.
H.C.F. (Highest Common Factor): The greatest positive integer that divides two or more given numbers without leaving a remainder.

Formulas:

Product of two numbers = L.C.M. of the two numbers * H.C.F. of the two numbers
H.C.F. of two numbers = (Product of the two numbers) / (L.C.M. of the two numbers)

In this question, we have used the second formula to derive the expression for the H.C.F. of x and y.

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5 Comments

Gaurav 2019-10-28 10:04:31

Too easy

Bargavi V 2018-10-09 08:54:55

Solution;

Product of two numbers
=HCFÃ—LCM

Here product of two numbers is XY and LCM =Z
then,
We have to apply the formula

XY=HCFÃ—Z

XY/Z=HCF

Nasrin shaikh 2018-09-18 08:45:47

HCF Ã— LCM of two numbers = Product of the given two numbers.

x Ã— y = z Ã— other number.

Other number = xÃ—y / z.

Ans: D.

VENKATESWARLU 2018-07-22 12:58:48

If u take any two natural number i. e.,, for example we take x=2 and y=4 then lcm of two numbers is 4 that is z. So z=4 and hcf of 2and 4 is 2 in answers option we will place x and y options xy/z is 2(4)/2=4. In first we assume two values x=4,y=2 will satisfies that equation so its the correct option

josh 2017-06-14 05:33:00

ans is : xy/z.

for eg: lets take values for x and y. x=2 and y=3.
now their lcm is 6.
if we want to find hcf =(2*3)/6=1 (we know that lcm of 2 n 3 is 1 since both are coprimes).
another eg: x=4, y=8
now their lcm is 8
to find hcf=(4*8)/8=4
we have one formula related to this,
product of two numbers=product of lcm and hcf
x*y=lcm of (x,y)* hcf of (x,y)