LCM and HCF MCQ | Page 5 of 5 | with Solutions for Competitive exams

21. The L.C.M. of two numbers is 20 times their H.C.F. The sum of H.C.F. and L.C.M. is 2520. If one of the numbers is 480, the other number is :

a) 400 b) 520 c) 480 d) 600

Correct Answer: (d)
Using Rule 1,
1st number × 2nd number = L.C.M. × H.C.F
Let the H.C.F. be H.
L.C.M. = 20H
Then, H + 20H = 2520
⇒ 21 H = 2520
⇒ H = 2520/20 = 120

∴ L.C.M. = 20H = 20×120= 2400
As, First number × Second number = L.C.M. × H.C.F.
⇒ 480 × Second number = 2400 × 120
⇒ Second number = (2400×120)/480 = 600

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22. The H.C.F. of two numbers, each having three digits, is 17 and their L.C.M. is 714. The sum of the numbers will be:

a) 289 b) 221 c) 391 d) 731

Correct Answer: (b)
Let the numbers be 17x and 17y
where x and y are co-prime.
LCM of 17x and 17y = 17 xy
According to the question,
17xy = 714
⇒ xy = 714/14 = 42 = 6 x 7
⇒ x = 6 and y = 7
or, x = 7 and y =6.
First number = 17x = 17 × 6 = 102
Second number = 17y =17 × 7 = 119
∴ Sum of the numbers = 102 + 119 = 221

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23. The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the numbers?

a) 8 and 6 b) 2 and 4 c) 8 and 10 d) 6 and 4

Correct Answer: (d)
Using Rule 1,
1st number × 2nd number = L.C.M. × H.C.F
Let the numbers be x and (x + 2).
∴ Product of numbers = HCF × LCM
⇒ x (x + 2) = 24
⇒ x2 + 2x – 24 = 0
⇒ x2 + 6x – 4x – 24 = 0
⇒ x (x + 6) – 4 (x + 6) = 0
⇒ (x – 4) (x + 6) = 0
⇒ x = 4, as x ≠ 6 = 0
∴ Numbers are 4 and 6.

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24. The sum of two numbers is 45. Their difference is 1 9 of their sum. Their L.C.M. is

a) 200 b) 100 c) 250 d) 150

Correct Answer: (b)
Let the number be x and y.
According to the question,
x + y = 45 ……… (i)
Again, x – y = 1/9 ( x + y )
x – y = 1/9 x 45
or x – y = 5 ….. (ii)
By (i) + (ii) we have,
x + y = 45
x – y = 5
—–
2x
= 50
or, x = 25
y = 45 – 25 = 20.
Now, LCM of 25 and 20 = 100.

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25. A number x is divisible by 7. When this number is divided by 8, 12 and 16. It leaves a remainder 3 in each case. The least value of x is:

a) 148 b) 150 c) 149 d) 147

Correct Answer: (d)
LCM of 8, 12 and 16 = 48
∴ Required number
= 48a + 3 which is divisible by 7.
x = 48a + 3 = (7 × 6a) + (6a + 3) which is divisible by 7.
i.e. 6a + 3 is divisible by 7.
When a = 3, 6a + 3 = 18 + 3 = 21
which is divisible by 7.
∴ x = 48 × 3 + 3 = 144 + 3 = 147

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We hope the insights provided in this page regarding MCQ on LCM & HCF have been helpful for your preparation. LCM HCF forms the base for solving many questions in quantitative aptitude in short cut, which makes this chapter very important while preparing for competitive exam. Visit our other MCQ pages to practice more objective type questions.

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