# HCF and LCM Quiz Set 002

### Question 1

Three lights are flashing at regular intervals. They, respectively, flash after 18, 36 and 54 seconds. How many times do they together flash in 1836 seconds?

A

18 times.

B

19 times.

C

17 times.

D

20 times.

Soln.
Ans: a

They will together flash after the LCM of their times. The LCM of 18, 36 and 54 = 108. So they will flash 1 + \$1836/108\$ = 18 times.

### Question 2

Which is the least number which must be added to 4196 so that it becomes divisible by 24, 50 and 105?

A

4.

B

5.

C

3.

D

6.

Soln.
Ans: a

The LCM of 24, 50 and 105 = 4200. The lcm when divided by either of these numbers leaves the remainder 0. The minimum number to be added is 4200 - 4196 = 4.

### Question 3

What is the LCM of \${6/13}\$, \$3{3/5}\$ and \${2/9}\$?

A

18.

B

19.

C

20.

D

21.

Soln.
Ans: a

The LCM of numerators 6, 18 and 2 is 18. The HCF of denominators 13, 5 and 9 is 1. So the required LCM of the given fractions is 18/1 = 18.

### Question 4

Which is the smallest number which when divided by 15, 9 or 16 leaves 9, 3, 10 as the respective remainders?

A

714.

B

715.

C

713.

D

716.

Soln.
Ans: a

By inspection, the difference between the numbers and their respective remainders is same = 6. The LCM of 15, 9 and 16 = 720. So the required number is 720 - 6 = 714.

### Question 5

The HCF of two numbers is 7. The factors of their LCM are 7, 13 and 5. Which is the greater of the two numbers?

A

91.

B

182.

C

45.

D

273.

Soln.
Ans: a

The numbers are 7 × 13 = 91, and 7 × 5 = 35. The greater of them is 91. 