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# If the LCM of A and B is 72 and their HCF is 6, what is the

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Intern
Joined: 09 Feb 2012
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If the LCM of A and B is 72 and their HCF is 6, what is the  [#permalink]

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20 Aug 2012, 11:52
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If the LCM of A and B is 72 and their HCF is 6, what is the product of A & B?

Thanks guys!

OA: 432
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Joined: 02 Sep 2009
Posts: 50583
Re: If the LCM of A and B is 72 and their HCF is 6, what is the  [#permalink]

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20 Aug 2012, 11:57
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NYC5648 wrote:
If the LCM of A and B is 72 and their HCF is 6, what is the product of A & B?

Thanks guys!

OA: 432

The most important property of LCM (the least common multiple) and GCD (the greatest common divisors) is: for any positive integers $$x$$ and $$y$$, $$x*y=GCD(x,y)*LCM(x,y)$$, so AB=72*6=432.

Questions to practice:
if-x-and-y-are-positive-integers-is-xy-a-multiple-of-102540.html
if-x-and-y-are-positive-integers-what-is-the-value-of-xy-95872.html
if-the-least-common-multiple-of-integers-x-and-y-is-105745.html#p827452 (Karishma's post explaining this property)

Hope it helps.
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Re: If the LCM of A and B is 72 and their HCF is 6, what is the  [#permalink]

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01 Oct 2012, 03:09
LCM of two numbers x GDF of the two numbers = Product of the two numbers ...

Therefore Product of A and B = 432 ...
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Re: If the LCM of A and B is 72 and their HCF is 6, what is the  [#permalink]

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15 Feb 2013, 07:21
Example:
You have two numbers x=8 and y=12.
LCM of x,y = 24
GCF of x,y = 4

(LCM of x and y) X (GCF of x and y) = XY
24 X 4 = 8 X 12
96 = 96
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Re: If the LCM of A and B is 72 and their HCF is 6, what is the  [#permalink]

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15 Feb 2013, 08:14
Product A*B= lcm*hcf(gcd)= 72*6= 423
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Re: If the LCM of A and B is 72 and their HCF is 6, what is the  [#permalink]

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15 Feb 2013, 08:49
1
Try to understand why is so.

take two numbers a and b

The prime factorization of those numbers is

a= d,d,e,r
b=d,e,g,h,i

HCF of a and b = d,e
LCM of a and b = d,e,d,r,g,h,i
Product of HCF and LCM = d.e.d.e.d.r.g.h.i ---------> d^3.e^2.r.g.h.i
Product of Numbers = d.d.e.r.d.e.g.h.i --------------> d^3.e^2.r.g.h.i

in my opinion it is better to understand any theorem/rule than to remember it.

Hope it clears!

Regards,

Abhijit.
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If the LCM of A and B is 72 and their HCF is 6, what is the  [#permalink]

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08 Sep 2018, 02:49
The product of any two positive integers x and y is equivalent to the product of the square of their hcf and other individual numbers,or the product of their lcm and hcf.
X*Y=HCF^2 * P =LCM*HCF
where P is other individual numbers(i.e let's say X = 6:1*2*3 and Y =8:1*2*2*2, the hcf of X and Y is 2 and P is 1*3*1*2*2)
therefore X*Y =LCM*HCF= 72*6 =432
If the LCM of A and B is 72 and their HCF is 6, what is the &nbs [#permalink] 08 Sep 2018, 02:49
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