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SIXTH GRADE / GREATEST COMMON DIVISOR and LEAST COMMON MULTIPLE / TEST 3.1.2

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH.
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

SOME OF OUR QUESTIONS ARE REALLY HARD, FOR THOSE THAT ARE SKILLED IN MATH.
SKIP THEM IN CASE NOT FOR YOU.

IF YOU DESIRE SO, WE CAN DISCUSS HARD/INTERESTING QUESTIONS IN OUR FORUM.

 GCD and LCM

    ♦ 
We preferred to introduce htese concepts earlier.
    ♦ We believed if a rational number is to be reduced, GCD is to be used.
    ♦ If the denominators are to be equal, the LCM is to be looked for.

    Ref.-1
    Ref.-2
1. Given the 24-digit number 333...333 and 49-digit number 222...222. What will be the LCM of the residues if they both are divided by 9 ?

!

a) No GCM
b) 33
c) 2
d) 3
72 = 8x9 + 0 and 98 = 10x9 + 8 .
2. What will be the LCM of all possible A's if A ∈ {digits} ?

a) 275
b) 444
c) 425
d) 315
LCM of 1,3,5,7, and 9 = ?
3. How do we need to change the second number if we want 324 and 126 relatively prime after a minimal change ?

a) increase by 1
b) increase by 2
c) decrease by 2
d) decrease by 1
Change means increase or decrase.
4. Prime factorization of the number 36 is below. Which of the following choices is the set of its divisors ?

!

a) {1,2,3,4,6,9,12,18}
b) {1,2,3,4,6,9,12,18,36}
c) {2,3,4,6,9,12,18,36}
d) {2,3,4,6,9,12,18}
In order to find the number of divisors we need to consider the powers of prime factors; we just add 1 to each power and we multiply them; i.e. (2+1)x(2+1) = 3 x 3 = 9 gives the number of divisors since the number 36 = 22 x 32.
5. Which of the followings is the set of numbers having 1 as GCD and 36 as LCM ?

a) {{1,36} , {2,18} , {4,9}}
b) {{1,36}}
c) {{1,36} , {4,9}}
d) {{4,9}}
Find the divisors of 36 and choose the ones having ...
y
6. 2 tractors moving with constant veleocities v1 and v2 begin to take the distance between 2 villages in opposite directions and simultaneously. They confront at a certain point and times elapsing after this point (hours) are numbers having 36 and 1 as the LCM and GCD. How much time is supposed to elapse after confrontation for the slower tractor to reach its destination ?

!

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2



a) 6
b) 14
c) 9
d) 5


This is a question asked in a mathematical competition. We hardened it a little bit. Congrats to who are able to solve .
The product of GCD and LCM should be the product of the numbers in question. So the elapsed times should be divisors of 36. These are given, the propers are given, in the answer to question 5.
The case of 1 and 36 is not very likley but it does not change the answer. Have a look at ry1.
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. The numbers 6 and 10 have a GCD of 2. What is their LCM ?

a) 20
b) 30
c) 15
d) 60
The product of the numbers is also the product of GCD and LCM. So the question is 60/2 = ?
8. Two numbers have a GCD and a LCM as 4 and 50. What is the other number if one is 25 ?

a) 4
b) 6
c) 10
d) 8
The product of the numbers should be 200 .
9. The thousands' of populations of 3 different villages are 3 consecutive digits. What is their (the digits') GCD ?

!


a) 2
b) 3
c) 1
d) 5
GCD of 3 consecutive digits is being questioned. Let them be 1, 2 and 3 as a case .
10. How many positive factors should the number 625 x n4 have if n ∈ {2,3,7,11,13,17,19,23} ?

a) 25
b) 30
c) 20
d) 15
54 x n4 means it should have (4+1)x(4+1) = ... factors .
11. In which interval will the sum of 2 numbers be if their LCM is 18 ?

a) 12 and 18
b) 17 and 11
c) 19 and 11
d) 20 and 12
Two possible cases : Pairs are 1;18 or 2;9 . The pair 3;6 has 6 as LCM .
y
12. What will be the LCM of the number 128 and the number of divisors of 720 that are divisible by 8 and not by 9 ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2".

RY1 RY2



a) 256
b) 128
c) 64
d) 512
720 = 8x9x10 = 23 x 32 x 10 = 24 x 32 x 5 and the number of its divisors is 5x3x2 = 30 . For further help have please a look at ry1.
13. What will be the sum of LCM and GCD of the numbers 17 and the one that gives a residue of 5 in case it divides 110, 170 and 185 ?

a) 256
b) 245
c) 255
d) 196
The second should be 15. Since 17 is prime, the GCD is 1 .
14. What will be the LCM of the greatest two common divisors of 150 and 180 ?

a) 20
b) 30
c) 25
d) 50


Divisors of 150: 1,2,3,5,6,10,15,25,30,50,75,150
Divisors of 180: 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
15. What will be the LCM of the number of elements of the sets of the divisors and the prime divisors of 360 ?

a) 12
b) 18
c) 22
d) 24
The number of divisors is 4x3x2 = 24 since 360=23 x 32 x 5 .
16. For April 23 Festival Turkey has 3 groups of visitors from 3 different countries each having 24, 42 and 54 people respectively. How many different rooms will be needed if people from different countries should stay in different rooms and each room is to have an equal number of visitors ?

!


a) 24
b) 20
c) 32
d) 30
The GCD is 6. For the group of 24 visitors 4 rooms are needed and ...
17. The number 561.. whose last 2 digits is not given is divisible by 30 and the greatest of such kind. What will be the GCD of this number and the greatest of its divisors (after itself) ?

a) 21 320
b) 24 750
c) 20 640
d) 28 095
The number should be 56 190 .
y
18. What will be the GCD of 27 and the number of divisors of 7 200 that are divisible by 8 and not by 9 ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2


a) 9
b) 8
c) 12
d) 18
We have derived in queation 12 of this test the divisors of 720; begin from there and find the divisors questioned. Look for help in ry1 .
19. One of the numbers that are relatively prime is the least 2-digit number and their LCM is 330. Which number is the other ?

a) 66
b) 44
c) 33
d) 25
The LCM is the product of the numbers because they are relatively prime .
20. What will be the product of 2 numbers whose LCM can be found as in the figure ?

!

a) 3 444
b) 2 466
c) 4 116
d) 3 816
LCM is clearly 7 and the GCD is 12x49 = 600 - 12 = 588 .
21. (40 , 44 , 48)GCD = ? or in another notation GCD(40, 44, 48) = ?

a) 8
b) 6
c) 4
d) 2
Division of these numbers by 4 gives 3 consecutives 10, 11 and 12 .
y
22. What is the product LCM(44,A) x GCD(44,A) if A is the number of divisors of 72 000 that are divisible by 8 and not by 9 ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) 2 400
b) 1 800
c) 1 716
d) 1 408


Begin with ry1 of question 18 and have a look at ry1 of this q. if needed .
23. 3 runners take 400 m. around the field respectively in 27, 30 and 33 seconds. How much time will it take till they get in line if they begin simultaneously and continue that long ?

!


a) 36 minutes
b) 49 1/2 minutes
c) 24 1/2 minutes
d) 66 minutes
Find the LCM of 27, 30 and 33.
24. What will be the the LCM according to the figure below ?

!


a) 2 205
b) 1 505
c) 1 755
d) 2 465
(50 - 1) x 45 = ?
25. What is the moral of story in the following figure ?

!


a) numbers are complex
b) numbers are perfect
c) numbers are relatively prime
d) numbers are whole
Two numbers are relatively prime if they do not have any common divisor .
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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