Question 1
1 Mark
If L.C.M. of two consecutive even numbers is 312, then what will be the sum of these two numbers?
Options
Option A
48
Option B
46
Option C
52
Option D is correct
50
Questions & Answers: "Factors and Multiples (HCF and LCM)"
Complete guide to "Factors and Multiples (HCF and LCM)" for Math students. Below you will find important questions and model answers to help you prepare.
7 Questions
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We are building a dedicated quiz for this topic, but you can test your skills on a similar concept: Geometry (Angles, Circles, and 3D Nets) - Scholarship-VIII Practice Set 1.
Question 2
1 Mark
Reena had some flowers. She prepared garlands from them. When she made every garland of 12 flowers, she was left with 11 flowers. If she had used 16 flowers for each garland then she would have left with 15 flowers. If she had used 18 flowers for each garland then she would have left with 17 flowers. Find the minimum number of flowers that she may have.
Options
Option A
161
Option B
155
Option C is correct
143
Option D
145
Question 3
1 Mark
Find the smallest number from the following such that when it is divided by every 1 digit prime number, every time the remainder is 1.
Options
Option A
106
Option B is correct
211
Option C
31
Option D
71
Question 4
1 Mark
If a number is divided by 18 then the remainder is 1, if it is divided by 24 then the remainder is 7 and if it is divided by 36 then the remainder is 19. What is the smallest such type of number?
Options
Option A
91
Option B
71
Option C
79
Option D is correct
55
Question 5
1 Mark
The LCM of two co-prime numbers is 910 and their sum is 83. What will be the difference between the two numbers?
Options
Option A is correct
57
Option B
60
Option C
81
Option D
75
Question 6
1 Mark
H.C.F of two digit two numbers is 14 and L.C.M. is 490. Find the sum of those two numbers.
Options
Option A
140
Option B
147
Option C is correct
168
Option D
182
Question 7
1 Mark
L.C.M. of two consecutive odd numbers is 8463. Find the bigger odd number out of the two numbers.
Options
Option A
91
Option B is correct
93
Option C
95
Option D
97
Explanation
Let the two consecutive odd numbers be and . Consecutive odd numbers are always coprime, meaning their greatest common divisor (HCF) is . For coprime numbers, their Least Common Multiple (LCM) is equal to their product. Given that the LCM is , we have . This is a quadratic equation . We can estimate by taking the square root of . . Since the numbers are consecutive odd integers, they must be close to . The two odd integers closest to with a difference of are and . Let's verify: . Thus, the two numbers are and . The bigger odd number is .