LCM and HCF MCQs

LCM and HCF
Factors and Multiples : All the numbers that divide a number completely, i.e., without leaving any remainder, are called factors of that number. For example, 24 is completely divisible by 1, 2, 3, 4, 6, 8, 12, 24. Each of these numbers is called a factor of 24 and 24 is called a multiple of each of these numbers … More on LCM and HCF

Question 1
Three friends started running together on a circular track at 8:00:00 am. Time taken by them to complete one round of the track is 15 min, 20 min, 30 min respectively. If they run continuously without any halts, then at what time will they meet again at the starting point for the fourth time ?
Cross
8:30:00 am
Cross
9:00:00 pm
Tick
12:00:00 pm
Cross
12:00:00 am
LCM    Numbers    
Discuss it


Question 1-Explanation: 
LCM (15, 20, 30) = 60 => They meet at the starting point after every 60 min, i.e., after every 1 hour. Therefore, they will meet at the starting point for the fourth time after 4 hours, i.e., at 12:00:00 pm.
Question 2
The LCM of two co-prime numbers is 117. What is the sum of squares of the numbers ?
Cross
220
Cross
1530
Tick
250
Cross
22
LCM    Numbers    
Discuss it


Question 2-Explanation: 
117 = 3 x 3 x 13 As the numbers are co-prime, HCF = 1. So, the numbers have to be 9 and 13. 92 = 81 132 = 169 Therefore, required answer = 250
Question 3
HCF of two numbers is 11 and their LCM is 385. If the numbers do not differ by more than 50, what is the sum of the two numbers ?
Tick
132
Cross
35
Cross
12
Cross
36
Numbers    LCM    HCF    
Discuss it


Question 3-Explanation: 
Product of numbers = LCM x HCF = 11 x 385 = 4235 Let the numbers be of the form 11m and 11n, such that \'m\' and \'n\' are co-primes. => 11m x 11n = 4235 => m x n = 35 => (m,n) can be either of (1, 35), (35, 1), (5, 7), (7, 5). => The numbers can be (11, 385), (385, 11), (55, 77), (77, 55). But it is given that the numbers cannot differ by more than 50. Hence, the numbers are 55 and 77. Therefore, sum of the two numbers = 55 + 77 = 132
Question 4
Two numbers are in the ratio of 5:7. If their LCM is 105, what is the difference between their squares ?
Tick
216
Cross
210
Cross
72
Cross
840
Numbers    LCM    HCF    
Discuss it


Question 4-Explanation: 
Let \'h\' be the HCF of the two numbers. => The numbers are 5h and 7h. We know that Product of Numbers = LCM x HCF => 5h x 7h = 105 x h => h = 3 So, the numbers are 15 and 21. Therefore, difference of their squares = 212 - 152 = 441 - 225 = 216
Question 5
Which of the following is the largest of all ? (i) 7/8 (ii) 15/16 (iii) 23/24 (iv) 31/32
Cross
(i)
Cross
(ii)
Cross
(iii)
Tick
(iv)


Question 5-Explanation: 
LCM (8, 16, 24, 32) = 96 7/8 = 84/96 15/16 = 90/96 23/24 = 92/96 31/32 = 93/96 Hence, 31/32 is the largest of all.
Question 6
Two numbers are in the ratio 3 : 5. If their L.C.M. is 75. what is sum of the numbers?
Cross
25
Cross
45
Tick
40
Cross
50


Question 6-Explanation: 
1st number = 3x
2nd number =5x
LCM of 3x and 5x is 15x
=> 15x = 75
=> x = 5
sum = 15+25 =40
Question 7
Ratio of two numbers is 3:2. If LCM of numbers is 60, then smaller number is?
Tick
20
Cross
30
Cross
40
Cross
50


Question 7-Explanation: 
say, 1st number =3x
2nd number =2x
LCM of numbers = 6x
given LCM = 60
=> x6 = 60
=>x = 10
Question 8
Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:
Cross
40
Tick
20
Cross
30
Cross
10


Question 8-Explanation: 
Let the numbers be 2x, 3x and 4x LCM = 12x 12x=240 ⇒x=20 H.C.F of 40, 60 and 80=20
Question 9
What is the lowest common multiple of 12, 36 and 20?
Cross
120
Tick
180
Cross
360
Cross
240


Question 9-Explanation: 
LCM = 180
Question 10

What is the least number which when divided by 4, 5, 6 and 7 leaves a remainder 3, but when divided by 9 leaves no remainder?

Cross

1683

Cross

1263

Cross

843

Tick

423



Question 10-Explanation: 

LCM of 4,5,6,7 is 420
=>(420k+3) should be divisible by 9 
if k =1, 423/9, remainder=0

When 423 is divided by 4, 5, 6, 7, it gives remainder 3 and when divided by 9 leaves a remainder 0.
So, the least number which when divided by 4, 5, 6 and 7 leaves a remainder 3, but when divided by 9 leaves no remainder is 423

There are 16 questions to complete.


  • Last Updated : 03 Oct, 2023

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