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Factors and Multiples

Description: Multiple choice questions on LCM and HCF
Number of Questions: 16
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Tags: LCM GCD HCF Math
Attempted 0/16 Correct 0 Score 0

If the greatest common factor (GCF) of two numbers is one of those numbers then their least common multiple(LCM) shall be

  1. The smaller of the two numbers

  2. The product of the two numbers

  3. The larger of the two numbers

  4. The difference of the two numbers

  5. None of the above


Correct Option: C
Explanation:

If the Greatest Common Factor (GCF) of two numbers is one of those numbers then their Least Common Multiple(LCM) shall be the larger of the two numbers.

For e.g. if the two numbers are 4 & 8 then HCF or GCF is 4 but LCM shall be 8.

If the greatest common factor of the two natural numbers is 1, we say that the numbers are

  1. Absolutely Prime

  2. Co-Prime or Relatively prime

  3. Twin Prime Numbers

  4. Whole numbers

  5. None Of these


Correct Option: B
Explanation:

Correct. Such pair of natural numbers are called Co-Prime or Relatively prime. For e.g. 28 (7x4) & 15 (3x5)

The GCF of two consecutive natural numbers is always _____

  1. 1

  2. 0

  3. Undefined

  4. All of these

  5. None of These


Correct Option: A
Explanation:

The GCF of two consecutive numbers is always one.

Take any two consecutive natural numbers and try out to factorise them.

Check the common factor..Its always 1.

Find the smallest number which, when divided by 3, 4 and 5 individually shall leave a remainder of 1?

  1. 21

  2. 61

  3. 46

  4. 60

  5. None of these


Correct Option: B
Explanation:

The answer is 1 greater than Least Common Multiple of 3, 4 and 5 which, when divided by them shall yield 1 as remainder. The LCM of 3, 4 & 5 is 60.

Therefore correct answer is 61.

The product of LCM and GCF of two natural numbers is equal to the _____ of the two numbers.

  1. SUM

  2. Difference

  3. Product

  4. All of these

  5. None of These


Correct Option: C
Explanation:

Correct.

Product of Two Natural Numbers = Their LCM x Their HCF

Find the smallest number which can be exactly divided by the numbers 18, 24 & 48.

  1. 48

  2. 72

  3. 64

  4. 96

  5. 144


Correct Option: E
Explanation:

Correct. The LCM of 18, 24 & 48 is 144.

Find the largest number that will divide 398, 436 and 542 leaving 7, 11 & 15 respectively as reminder.

  1. 23

  2. 25

  3. 31

  4. 17

  5. 51


Correct Option: D
Explanation:

Correct.

The answer is the GCD (Greatest Common Divisor) of the respective numbers subtracted by values of remainder 

i.e GCD of (398 - 7), (436 - 11), (542 - 15) .

Which is 17.

Find the smallest number which, when divided by 25, 40 & 60 leaves a remainder of 7 in each case.

  1. 207

  2. 300

  3. 600

  4. 607

  5. 200


Correct Option: D
Explanation:

Correct.The answer is the number which is 7 more than the LCM of the three given numbers.

Hence, correct answer is 600 + 7 = 607.

The product of two numbers is 1260. If the LCM of the two numbers is 210, the HCF of the numbers shall be

  1. 6

  2. 210

  3. 42

  4. 30

  5. 21


Correct Option: A
Explanation:

Correct.

For the two numbers, their Product = LCM x HCF.

Therefore, HCF = (Product of two numbers) / (LCM) 

i.e.  HCF = 1260 / 210 = 6

Statement: Two numbers can have their HCF as 14 & LCM as 204.

Based on above statement select the correct alternative.

  1. Yes, they can

  2. Yes, these numbers are 56 & 51

  3. The statement is partially true

  4. The statement is partially false

  5. Absolutely no


Correct Option: E
Explanation:

Correct. HCF is always a factor of LCM.

A cat and mouse are descending from the ladder of eternity. The cat can jump 10 steps at a time and the mouse descends by jumping 4 steps at a time. The mouse is at 24th step when cat starts from the top of the ladder. At which step from top does the cat catches the mouse.

  1. 30

  2. 40

  3. 60

  4. 80

  5. 120


Correct Option: B
Explanation:

Correct.

The essence of the question is least common multiples of two numbers.

If the ladder of eternity would have been a circular one and the cat & mouse constantly running they might have always met at steps at common multiples like 40, 80, 120, 160 etc.

Mohan works at a bakery. He must box 30 cakes, 24 pastries, and 48 biscuits so that all of the boxes have the same number of each. What is the greatest number of boxes he can use?

  1. 8

  2. 6

  3. 12

  4. 4

  5. 2


Correct Option: B
Explanation:

Correct. 

The correct answer is the GCD of the 3 food items which is 6. 

Thus there will be 5 cakes, 4 pastries and 8 biscuits in each of the 6 boxes.

Miss Gayatri's class has 12 girls and 20 boys. She wants to divide the students into groups so that, every student is in a group, each group has the same number of girls and each group has the same number of boys. What is the greatest number of groups that she can make?

  1. 4

  2. 2

  3. 3

  4. 5

  5. 6


Correct Option: A
Explanation:

Correct.

The answer is GCD of the number of girls and boys, which is 4.

An ice-cream vendor is taking continuous rounds of a residential colony on a tricycle cart. He passes Gautam's house after every 30 minutes. A fruit seller walking with his cart takes rounds on the same path and passes Gautam's house in every 50 minutes. If Gautam buys ice-creams and fruits from both of them together and the two start from his house at the same time, after how many minutes again will they pass simultaneously toghether in-front of Gautam's house.

  1. 120

  2. 90

  3. 150

  4. 160

  5. 140


Correct Option: C
Explanation:

Correct.

The next simultaneous appearance of two infront of Gautams house will be a least common multiple of the times taken by both the vendors.

i.e. LCM of 30 & 50.

Which is 150.

A rectangular field measures 480 m x 144 m and is to be paved with square tiles. The owner wants the field to be paved with SQUARE tiles with MAXIMUM covering area. Find the size of such a square tile and the total number of tiles equired to completely pave the field.

  1. 96 & 7 respectively

  2. 24 & 120 respectively

  3. 48 & 30 respectively

  4. 36 & 54 respectively

  5. 72 & 7 respectively


Correct Option: C
Explanation:

Correct.

The maximum size of square tile shall be equal to the Greatest Common Divisor (GCD) of the length and breadth, i.e. 480, 144, which is 48. 

The total no. of tiles is = 480 x 144/(48 X 48) = 30.

Mr. Milkha runs around a track in 30 seconds and I can run around the track in 40 seconds. If we both start at the same time how many seconds will it be until we both cross the starting line together?

  1. 60

  2. 90

  3. 120

  4. 180

  5. 100


Correct Option: C
Explanation:

Correct.

Mr Milkha and I will take round trips when at 120 seconds (LCM of the two time periods) from start time he will meet me again at the start line. 

While he is starting his 5th round I will start my 4th.

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