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

achloes · Answer

avigutman

Would you mind sharing your approach to this question? I'm stumped by the ratio part.

bumpbot · Answer

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

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