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If the LCM of two numbers a and b is 1104 and their HCF is 4

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ricsingh
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If the LCM of two numbers a and b is 1104 and their HCF is 4 [#permalink] New post  Updated on: 10 Apr 2014, 01:42
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If the LCM of two numbers a and b is 1104 and their HCF is 4, which of the following MUST be true?

I. a * b = 4416
II. a and b are both divisible by 8
III. a : b = 48 : 23

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III
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Originally posted by ricsingh on 09 Apr 2014, 10:24.
Last edited by Bunuel on 10 Apr 2014, 01:42, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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If the LCM of two numbers a and b is 1104 and their HCF is 4 [#permalink] New post  10 Apr 2014, 02:05
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ricsingh wrote:
If the LCM of two numbers a and b is 1104 and their HCF is 4, which of the following MUST be true?

I. a * b = 4416
II. a and b are both divisible by 8
III. a : b = 48 : 23

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III


One of the most important properties of LCM (the least common multiple) and GCD (the greatest common divisor) is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\), so ab = 1104*4 = 4416. Hence option I is in fact true.

Since the greatest common divisor of the two numbers is 4, then at least one number is NOT divisible by 8. Hence II must not be true.

As for III: one number can be 4 and another 1,104, their ratio is not 48:23, thus III must not be true.

Answer: A.

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P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 5 and 7. Thank you.
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Re: If LCM of two number x and y is 1104 and HCF is 4, which of [#permalink] New post  09 Apr 2014, 10:48
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On first sight, this question might look difficult, but if you read through the choices, it's fairly easy.

Look at a. Yeah, who knows. Skip!

Look at b. This answer choice doesn't make any sense. If "x:y = 48:23" is a true statement, there's nothing preventing "x:y = 23:48" from being a true statement either. Thus it's false.

At this point, the answer is "a only" because everything else includes b.

c makes no sense either because we are already given that HCF is 4... if c was true, the HCF would b 8 (or a multiple of 8)
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Re: If LCM of two number x and y is 1104 and HCF is 4, which of [#permalink] New post  09 Apr 2014, 11:16
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ricsingh wrote:
If LCM of two number x and y is 1104 and HCF is 4, which of the following must be true.

a. x*y = 4416
b. x:y = 48:23
c. x and y are both divisible by 8


1. a only
2. b only
3. a and b only
4. b and c only
5. a, b and c


LCM (x,y)=1104
HCF (x,y)=4

The product of two numbers is equal to product of their LCM and HCF.

x * y =1104 * 4 =4416 so statement A is true

Since HCF (x,y) is 4 hence maximum common number with which x and y are divisible by is 4
so statement B is false

Now the ratio between x and y may be either 48:23 or 23:48
so statement C is false

Hence answer is 1
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If the LCM of two numbers a and b is 1104 and their HCF is 4 [#permalink] New post  26 Jul 2014, 06:53
Bunuel wrote:
ricsingh wrote:
If the LCM of two numbers a and b is 1104 and their HCF is 4, which of the following MUST be true?

I. a * b = 4416
II. a and b are both divisible by 8
III. a : b = 48 : 23

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III


One of the most important properties of LCM (the least common multiple) and GCD (the greatest common divisor) is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\), so ab = 1104*4 = 4416. Hence option I is in fact true.

Since the greatest common divisor of the two numbers is 4, then at least one number is NOT divisible by 8. Hence II must not be true.

As for III: one number can be 368 and another 12, their ratio is not 48:23, thus III must not be true.

Answer: A.

Similar questions to practice:
if-the-lcm-of-a-and-b-is-72-and-their-hcf-is-6-what-is-the-137562.html
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
what-is-the-value-of-integer-x-166423.html
set-q-contains-p-numbers-where-p-1-what-is-the-ratio-105981.html
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

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 5 and 7. Thank you.

Hi Bunuel,
Can you elaborate a little more on how to eliminate point iii ?
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Re: If the LCM of two numbers a and b is 1104 and their HCF is 4 [#permalink] New post  27 Jul 2014, 17:47
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ronr34 wrote:
Bunuel wrote:
ricsingh wrote:
If the LCM of two numbers a and b is 1104 and their HCF is 4, which of the following MUST be true?

I. a * b = 4416
II. a and b are both divisible by 8
III. a : b = 48 : 23

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III


One of the most important properties of LCM (the least common multiple) and GCD (the greatest common divisor) is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\), so ab = 1104*4 = 4416. Hence option I is in fact true.

Since the greatest common divisor of the two numbers is 4, then at least one number is NOT divisible by 8. Hence II must not be true.

As for III: one number can be 368 and another 12, their ratio is not 48:23, thus III must not be true.

Answer: A.

Similar questions to practice:
if-the-lcm-of-a-and-b-is-72-and-their-hcf-is-6-what-is-the-137562.html
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
what-is-the-value-of-integer-x-166423.html
set-q-contains-p-numbers-where-p-1-what-is-the-ratio-105981.html
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

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 5 and 7. Thank you.

Hi Bunuel,
Can you elaborate a little more on how to eliminate point iii ?


To eliminate E we should find a counterexample. 368 and 12 is one of counterexamples. Another one, probably easier one would be 4 and 1,104.
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Re: If the LCM of two numbers a and b is 1104 and their HCF is 4 [#permalink] New post  10 Sep 2014, 05:17
If NONE had been one of the answer option,then the difficulty rate would have definately shooted up..! :-D
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Re: If the LCM of two numbers a and b is 1104 and their HCF is 4 [#permalink] New post  10 Sep 2014, 05:38
Bunuel wrote:
To eliminate E we should find a counterexample. 368 and 12 is one of counterexamples. Another one, probably easier one would be 4 and 1,104.

Hi Bunuel,

Forgive me but could you clarify how one can make the relation between GCF and LCM, and the ratio of A:B? I understand that 368 and 12 are divisors of 1104 and 4, but I fail to see how these relate to the given GCF and LCM.

Thanks in advance!
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If the LCM of two numbers a and b is 1104 and their HCF is 4 [#permalink] New post  22 Oct 2020, 02:56
I. The product of two numbers is equal to the product of its GCF and LCM. This must be true.

II. We know that their GCF is 4; thus, both numbers can't be divisible by 8. False.

III. The numbers don't necessarily have to be in this ratio. False.

Answer is A.
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Re: If the LCM of two numbers a and b is 1104 and their HCF is 4 [#permalink] New post  21 Feb 2022, 23:50
If the LCM of two numbers a and b is 1104 and their HCF is 4, which of the following MUST be true?

I. a * b = 4416

Rule: Product of two integers = Product of their LCM and HCF

so, ab = 1104*4 = 4416 (True)

II. a and b are both divisible by 8

Since, the HCF of both a and b is 4, it cannot be true either. (False)

III. a : b = 48 : 23

\(\frac{a}{b}\) = \(\frac{48}{23}\) = \(\frac{2^4*3}{23}\)

LCM of a and b = 1104 = \(2^4*3*23\)

Therefore, this cannot be True either because we cannot have further higher powers of 2,3 and 23. And we would need so to make the product of a and b equal to 4416. (Hence, False)
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Re: If the LCM of two numbers a and b is 1104 and their HCF is 4 [#permalink]
21 Feb 2022, 23:50
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