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

Question

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

Bunuel · Accepted Answer

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. 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.

farful · Answer

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)

singage · Answer

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

ronr34 · Answer

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

Bunuel · Answer

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.

vards · Answer

If NONE had been one of the answer option,then the difficulty rate would have definately shooted up..! :-D

Armada0023 · Answer

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!

Basshead · Answer

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.

bv8562 · Answer

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 )

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards