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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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NYC5648
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If the LCM of A and B is 72 and their HCF is 6, what is the [#permalink] New post   20 Aug 2012, 12:52
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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!

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OA: 432
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Re: If the LCM of A and B is 72 and their HCF is 6, what is the [#permalink] New post   20 Aug 2012, 12:57
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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!

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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] New post   01 Oct 2012, 04:09
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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] New post   15 Feb 2013, 08:21
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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] New post   15 Feb 2013, 09:14
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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] New post   15 Feb 2013, 09:49
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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] New post   08 Sep 2018, 03:49
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
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Re: If the LCM of A and B is 72 and their HCF is 6, what is the [#permalink] New post   23 Jan 2020, 20:30
nk9285 wrote:
Product A*B= lcm*hcf(gcd)= 72*6= 423


I believe you refer to 432 instead of 423.
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Re: If the LCM of A and B is 72 and their HCF is 6, what is the [#permalink] New post   24 Jan 2020, 11:01
aaronlcr93 wrote:
nk9285 wrote:
Product A*B= lcm*hcf(gcd)= 72*6= 423


I believe you refer to 432 instead of 423.

Must be so , if you consider the units digit 2*6 = Units digit 2
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Re: If the LCM of A and B is 72 and their HCF is 6, what is the [#permalink] New post   08 Jun 2020, 05:34
One way I visualize GCD*LCM=a*b is by thinking about the two numbers' prime box (set of prime factors):
e.g.
70: 2 5 7
30: 2 3 5

GCD: pull out mutual factors: 2 5; multiply = 10 = GCD
LCM: pull out all factors and cross out duplicated ones: 2 5 7 X 3 X; multiply = 210 = LCM.
Notice the crossed-out factors in LCM are actually the ones in GCD. Thus, when you GCD * LCM, you reunite all factors, getting you back to a * b.

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] New post   22 Oct 2020, 02:58
The product of two numbers is equal to the product of its GCF and LCM.

72 * 6 = 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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