Previous year Quant quiz on HCF and LCM

1.Find that smallest number which when diminished by 11 is completely divisible by 14, 15, 21, 32 and 60.

(a)1681

(b)1679

(c)3371

(d)3349

2.The sum of two numbers is 36 and their G.C.D. is 4. How many such pairs are possible?

(a)1

(b)2

(c)3

(d)4

3.The sum of two numbers is 320 and their L.C.M. is 1584. What are those numbers?

(a)144, 176

(b)180, 140

(c)134, 186

(d)160, 140

4.The L.C.M. of two numbers greater than 29 is 4147 and their H.C.F. is 29. What is the sum of those number?

(a)966

(b)696

(c)669

(d)666

5.The H.C.F. and L.C.M. of two numbers is 13 and 455. If one of the number is between 75 and 125 then it is

(a)78

(b)104

(c)91

(d)117

6.The difference of two number whose L.C.M. and H.C.F. is same will be 

(a)0

(b)1

(c)can’t be determined

(d)None of these

7.The sum of two numbers is 377. If the sum and the difference of their L.C.M. and H.C.F. are respectively 2665 and 2639 then the numbers are

(a)144, 156

(b)130, 143

(c)117, 234

(d)156, 221

8.The L.C.M of two numbers is 45 times their H.C.F. If one numbers is 125 and the sum of their L.C.M and H.C.F. is 1150 then the other number is  

(a)225

(b)270

(c)315

(d)180

9.The L.C.M. of two numbers is 10 times their H.C.F. The sum of their L.C.M. and H.C.F. is 330. If one of the number is 60 then what is the other number?

(a)180

(b)150

(c)250

(d)90

10.The L.C.M. of two numbers is 56 times their H.C.F. The sum of the L.C.M. and H.C.F. of these numbers are 2565. If one of the number is 315 then what is the other number?

(a)450

(b)360

(c)450

(d)495

Answers and Solution:
1. (c)
Required number = (LCM. of 14,15,21,32 and 60) + 11
 = 3360 + 11 = 3371

2. (c)
Let, numbers are 4x and 4y
so, 4x + 4y = 36
or, x + y = 9
so (x,y) = (1,8),(2,7),(4,5) so total 3 pairs are possible

3. (a)
4. (b)
Let, numbers are 29a and 29b where a and b are co-prime numbers.
From the question , 29ab = 4147, ab = 143 = 13*11
so, the sum of numbers = 29a + 29b = 29(a+b) = 29(13+11)
= 29 * 24 = 696

5. (c)
6. (a)
7. (d)
8. (a)
Let, H.C.F = x so, L.C.M = 45x
from the question  x + 45x = 1150
or, x = 25 = G.C.F and 45x = 1125 = L.C.M
for two numbers, (G.C.F * L.C.M) = (product of numbers)
so 25 * 1125 = 125 * second number
so second number = 225

9. (b)
10. (b)