If the least common multiplier of positive integers A and B is 120 and

Question

If the least common multiplier of positive integers A and B is 120 and the ratio of A and B is 3:4, what is the largest common divisor of A and B?

A. 8
B. 9
C. 10
D. 12
E. 15

The least common multiplier of A and B is 120, the ratio of A and B is 3:4, what is the largest common divisor?

EgmatQuantExpert · Accepted Answer

Solution  
   Given:     
 • A: B = 3: 4
• LCM of A and B = 120

To find:     
 The GCD of A and B

Approach and Working Out:     
 • We can say that A = 3x and B = 4x
• This implies, the GCD of A and B = x, since 3 and 4 are co-primes.

We also know that, LCM (A, B) * GCD (A, B) = A * B
 • 120 * x = 3x * 4x
• Therefore, x = 10

Hence, the correct answer is Option C.

Answer: C

BrentGMATPrepNow · Answer

One approach is to find values of A and B that meet the given conditions.

The least common multiple of positive integers A and B is 120  
So, it COULD be the case that: A = 120 and B = 120, or A = 120 and B = 60, or A = 40 and B = 30, etc

The ratio of A and B is 3:4  
So, it could be the case that A =  30  and B =  40

What is the largest common divisor of A and B?  
The largest common divisor of  30  and  40  is 10

Answer: C

Cheers,
Brent

EncounterGMAT · Answer

HCF=?

We know HCF * LCM = The number A *B (product)
LCM = 120 and  \frac{A}{B} =\frac{3x}{4x}

=> HCF*120=3x*4x

HCF= \frac{12x^2}{120}  =  \frac{x^2}{10}

Trying out options to solve the equation could help. Since HCF ≠ fraction, the option which equals to integer is the answer.

A. 8 = \frac{8^2}{10}  = integer? NO

B. 9 = \frac{9^2}{10}  = integer? NO

C. 10 = \frac{10^2}{10}  = integer? YES

D. 12 = \frac{12^2}{10}  = integer? NO

E. 15 = \frac{15^2}{10}  = integer? NO

Therefore, IMO answer is  option C

effatara · Answer

We know that A*B=120x where 'x' is an integer.
We also know that A=3x and B=4x since A:B=3:4. Thus, A*B=12x^2
Therefore, 120x=12x^2....> x=10
Thus, A=30 & B=40

HCF of A and B is the product of their common divisors.
Divisors of A are 3, 2 & 5
Divisors of B are 2,2,2 & 5.
Divisors common to A and B are 2 & 5.
HCF of A and B is 2*5=10.

ANS: C

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 least common multiplier of positive integers A and B is 120 and

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 least common multiplier of positive integers A and B is 120 and

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