# LCM & HCF

Quantitative Aptitude Questions and Answers section on “LCM & HCF” with solution and explanation for competitive examinations such as CAT, MBA, SSC, Bank PO, Bank Clerical and other examinations.

1.

The LCM of two numbers is 30 and their HCF is 5. One of the numbers is 10. The other is:
[A]20
[B]15
[C]5
[D]25

15
Because, First number $\times$ Second number = LCM $\times$ HCF
Let the Second Number be x.
∴ 10x = 30 $\times$ 5
$=>x=\frac{30\times 5}{10}=15$
Hence option [B] is the right answer.

2.

The LCM of two numbers is 1820 and their HCF is 26. If one number is 130 then the other number is :
[A]1264
[B]1690
[C]364
[D]70

364
Given that :
LCM of two numbers = 1820
HCF of those numbers = 26
and one of the number is 130, hence another number is :
$\frac{1820\times26}{130}=364$
Hence option [C] is the right answer.

3.

The HCF of two numbers is 16 and their LCM is 160. If one of the number is 32, then the other number is:
[A]96
[B]48
[C]112
[D]80

80
We know that, First number $\times$ Second number = LCM $\times$ HCF
$=>$Second Number $=\frac{16\times 160}{32}=80$
Hence option [D] is the right answer.

4.

The HCF of two numbers is 15 and their LCM is 300. If one of the number is 60, the other is:
[A]75
[B]65
[C]50
[D]100

75
Because, First number $\times$ Second number = LCM $\times$ HCF
∴ Second Number = $\frac{15\times 300}{60}=75$
Hence option [A] is the right answer.

5.

The HCF of two numbers 12906 and 14818 is 487. Their LCM is :
[A]600129
[B]800172
[C]400086
[D]200043

400086
Because product of two numbers = HCF $\times$ LCM
$=>$ 12906 $\times$ 14818 = LCM $\times$ 478
$=> LCM$ = $\frac{12906\times 14818}{478}=400086$
Hence option [C] is the right answer.

6.

The LCM of two numbers is 864 and their HCF is 144. If one of the number is 288, the other number is :
[A]144
[B]432
[C]1296
[D]576

432
Required number = $\frac{HCF\times LCM}{First number}$
$=\frac{864\times 144}{288} = 432$
So the second number is 432.
Hence option [B] is the right answer.

7.

The HCF and LCM of two numbers are 12 and 336 respectively. If one of the number is 84, the other is :
[A]48
[B]36
[C]96
[D]76

48
First Number $\times$ Second Number = HCF $\times$ LCM
=> 84 $\times$ second number = 12 $\times$ 336
Since second number = $\frac{12\times 336}{84} = 48$
Hence option [A] is the right answer.

8.

The product of two numbers is 216. If the HCF is 6, then their LCM is :
[A]46
[B]48
[C]36
[D]76

36
Let the numbers be 6x and 6y where x and y are prime to each other.
$\therefore 6x \times 6y = 216$
$=> xy = \frac{216}{6\times 6} = 6$
$\therefore LCM = 6xy = 6 \times 6 = 36$
Hence option [C] is the right answer.

9.

The HCF and LCM of two numbers is 18 and 378 respectively. If one of the number is 54, then the other number is
[A]144
[B]196
[C]126
[D]236

126
Second Number $=\frac{HCF\times LCM}{First Number }$
$=\frac{18\times 378}{54} = 126$
Hence option [C] is the right answer.

10.

The HCF and product of two numbers are 15 and 6300 respectively. The number of possible pairs of the number is :
[A]3
[B]1
[C]4
[D]2

2
Let the number be 15x and 15y, where x and y are co-prime.
Since 15x $\times$15y = 6300
$=> xy = \frac{6300}{15\times 15} = 28$
So, two pairs are (7, 4) and (14, 2)
Hence the right option is [D].