H.C.F and L.C.M- Aptitude Questions and Answers

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The HCF and LCM of two numbers are 66 and 384 respectively. If the first number is divided by 2, the resulting answer is 66. The second number is?

A)
192

B)
196

C)
384

D)
576


Correct Answer :

192


Explanation :

First number= 66 * 2 = 132
132 * second number = HCF * LCM
132 * x = 66 * 384
x = 192

The LCM of two numbers is 280 and the ratio of the numbers of 7 : 8. Find the numbers?

A)
70 and 48

B)
42 and 48

C)
35 and 40

D)
28 and 32


Correct Answer :

35 and 40


Explanation :

Let the two numbers are 7x and 8x and LCM is 56x.
It is given that LCM = 280
ie, 56x = 280 and x = 5
hence,the numbers are 35 and 40.

HCF of 105, 150 and 210 is x, HCF of 126, 396,1080 is y and HCF of 440, 180 and 280 is z. Which of the following is greatest?

A)
x

B)
y

C)
z

D)
All are equal


Correct Answer :

z


Explanation :

HCF of 105, 150, 210
105 = 3 *8 *5 *7
150 = 2 *3 *5 *5
210 = 2 *3 *5 *7
x is = 3 *5 = 15
HCF of 126, 396, 1080
126 = 2 *3 *3 *7
396 = 2 *2 *3 *3 *11
1080 = 2 *2 *2 *3 *3 *3 *5
y is = 2 *3 *3 = 18
HCF of 440, 180, 280
440 = 2 *2 *2 *5 *11
180 = 2 *2 *5 *3 *3
280 = 2 *2 *2 *5 *7
z is = 2 *2 *5 = 20
Hence, z is maximum.

The five bells start ringing together and they toll at intervals of 6, 7, 8, 9 and 12 seconds respectively. After how many seconds will they toll together again?

A)
72

B)
612

C)
504

D)
318


Correct Answer :

504


Explanation :

Least common multiples (LCM) of ( 6, 7, 8, 9 and 12) = 504
So, they will toll together after 504 sec

A, B and C starts running in the same direction from the same point and the same time in a circular stadium . A completes one round in 252 seconds, B in 308 seconds, and C in 198 seconds. When will they meet again at the starting point?

A)
28 minutes 18 seconds

B)
42 minutes 36 seconds

C)
45 minutes

D)
46 minutes 12 seconds


Correct Answer :

46 minutes 12 seconds


Explanation :

Least common multiples (LCM) of (252 ,308 and 198) = 2772 sec
So, they will meet again together on starting point after on 46 minutes 12 seconds .

The LCM of two numbers is 520 and HCF is 4. If a number is 52,what will be the second number?

A)
40

B)
42

C)
50

D)
52


Correct Answer :

40


Explanation :

1st number ×2nd number = LCM × HCF

52 * 2nd number = 520 * 4
2nd number = (520 * 4)/52 = 40

The HCF and LCM of two natural numbers are 12 and 72 respectively. What is the difference between the two numbers, if one of the numbers is 24?

A)

12


B)

18


C)

21


D)

24



Correct Answer :

12


Explanation :

As we know that, First number * Second number = LCM * HCF
24 * Second number = 72*12
Second number = 72*12/24
Second number = 36

Difference between the two numbers = 36 − 24 = 12

The two numbers are 63 and 77, HCF is 7, Find the LCM?

A)

668


B)

693


C)

674


D)

680



Correct Answer :

693


Explanation :

LCM = 63 * 77 / 7 = 693

A natural number, when divided by 3, 4, 5, 6, and 7 respectively, leaves corresponding remainder of 2, 3, 4, 5 and 6. What is the smallest of all such numbers fulfilling the above condition ?

A)
2519

B)
419

C)
209

D)
839


Correct Answer :

419


Explanation :

Here 3 – 2 = 1, 4 – 3 = 1, 5 – 4 = 1, 6 – 5 = 1, 7 – 6 = 1
∴ The required Number = LCM of (3, 4, 5, 6, 7) – 1

2|3, 4, 5, 6, 7
3|3, 2, 5, 3, 7
|1, 2, 5, 1, 7

= (2*3*2*5*7) – 1
= 420 – 1
= 419

HCF and LCM of two numbers are 82 and 574 respectively. if one of the numbers is 287, find the second number?

A)
82

B)
164

C)
246

D)
41


Correct Answer :

164


Explanation :

H.C.F. × L.C.M. = First number × Second number

82 * 574 = 287 * Second number
Second number = 164

Find the smallest square number which is exactly divisible by 3, 5, 15, 18, 20 and 24?

A)
400

B)
900

C)
1600

D)
3600


Correct Answer :

3600


Explanation :

Factorize the numbers as

3 = 3
5 = 5
15 = 3*5
20 = 2*2*5
24 = 2*2*2*3

LCM = 2*2*2*3*5 = 120

Now for it to be a perfect square, it should have even powers. it’s need to 2*3*5 to make perfect square
Hence,
LCM = 2*2*2*2*3*3*5*5 = 3600

So the least perfect square divisible by all these given terms is 3600

The least number of five digits which is exactly divisible by 12,15 and 18 is?

A)
10010

B)
10015

C)
10020

D)
10080


Correct Answer :

10080


Explanation :

Least number of five digits is 10000
L.C.M of 12,15,18 is 180.
On dividing 10000 by 180,the remainder is 100
Therefore required number=10000+(180-100)
=10080

The least number which is perfect square and is divisible by each of the numbers 16, 20 and 24 is?

A)
216

B)
1600

C)
2400

D)
3600


Correct Answer :

3600


Explanation :

The least number divisible by 16,20,24 = L.C.M of 16,20,24=240
=2*2*2*2*3*5
To make it a perfect square it must be multiplied by 3*5
Therefore required number =240*3*5=3600

The largest four digit number which when divided by 4, 7 or 13 leaves a remainder of 3 in each case is?

A)

8739


B)
9831

C)
9834

D)
9893


Correct Answer :

9831


Explanation :

Greatest number of four digits is 9999
L.C.M of 4,7, and 13=364.
On dividing 9999 by 364 remainder obtained is 171.
Therefore greatest number of four digits divisible by 4,7,13
=9999-171=9828.
Hence required number=9828+3=9831.

Find the HCF and LCM of the polynomial x2-5x+6 and x2-7x+10?

A)

(x-2), (x-2)(x-3)(x-5)


B)
(x-2), (x-2)(x-3)

C)
(x-3), (x-2)(x-3)(x-5)

D)
none


Correct Answer :

(x-2), (x-2)(x-3)(x-5)


Explanation :

The given polynomials are
x^2-5x+6=0................1
x^2-7x+10=0...............2
we have to find the factors of the polynomials
x^2-5x+6
x^2-2x-3x+6
x(x-2)-3(x-2)
(x-3)(x-2)

x^2-7x+10
x^2-5x-2x+10
x(x-5)-2(x-5)
(x-2)(x-5)

From the above factors of the polynomial
the HCF as (x-2)and LCM as (x-2)(x-3)(x-5)

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