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

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PQRS is the greatest number of 4 digits which when divided by any of the numbers 6, 9, 12 or 17 leaves a remainder of 2 in each case. What is the value of (P + R)/(Q + S)?


PQRS, 4 अंकों की सबसे बड़ी संख्या है जो संख्या 6, 9, 12 या 17 द्वारा विभाजित में शेष 2 छोड़ देता है। तो (P + R)/(Q + S) का मान क्या है?

A)
18

B)
18/11

C)
11/18

D)
9/11


Correct Answer :

18/11


Explanation :

The required number, which is exactly divisible by each one of the given numbers, should be divisible by LCM of (6, 9, 12, 17) i.e. 612
The Largest number of four digits is 9999.by dividing 9999 to 612 get 207 as remainder.
So, the greatest number of 4 digits divisible by any numbers from 6, 9, 12 or 17 = (9999-207) = 9792.

But we should get the remainder as 2,so we need to add 2 to 9792.So the number PQRS is 9794.

Thus, required value (P + R)/(Q + S) = (9+9)/(7+4)
=>18/11

Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start ?


पांच घंटीयाँ क्रमश: 6, 5, 7, 10 और 12 सेकंड के अंतराल से बजती है। उन्‍होने एक निश्चित समय से एक साथ बजाना प्रांरभ किया। शुरुआती पहले घंटे को छोड़कर अगली बार सभी घंटीयाँ एक घंटे में कितनी बार एक साथ बजेंगी?

A)
7

B)
8

C)
9

D)
11


Correct Answer :

8


Explanation :

L.C.M. of 6, 5, 7, 10 and 12 is 420.

So, the bells will toll together after every 420 seconds i.e. 7 minutes.

Now, 7 x 8 = 56 and 7 x 9 = 63.

Thus, in 1-hour (or 60 minutes), the bells will toll together 8 times, excluding the one at the start.

The sum and difference between LCM and HCF of two numbers is 84 and 60 respectively. If one of the numbers is 24, find the other number?


दो संख्याओं के LCM और HCF के बीच योग और अंतर क्रमशः 84 और 60 है। यदि संख्याओं में से कोई एक संख्या 24 है, तो दूसरा नंबर क्या होगा।

A)
48

B)
36

C)
54

D)
16


Correct Answer :

36


Explanation :

As given,
LCM + HCF = 84 ----eq1
LCM - HCF = 60 ----eq2

When add eq1 and 2 then
2*LCM = 144
LCM => 72
after implement it in eq1, then
72 + HCF = 84
HCF = 84-72 =>12

LCM × HCF = Ist number ×IInd number Or Product of numbers = HCF × LCM
LCM = 72, HCF = 12
One number x = 24 ,Let other number be y
So, x*y = LCM * HCF
24 * y = 72 * 12
y = (72 * 12)/24 = 36
other number will be 36

The LCM and HCF of two numbers are 240 and 16 respectively. If the two numbers are in the ratio 3 : 5, the numbers are ?


दो नंबरों के लघुतम समापवतर्क(LCM) और महत्तम समापवर्तक(HCF) क्रमशः 240 और 16 हैं। यदि उनका अनुपात 3: 5 हैं, तो संख्याएं क्या हैं?

A)
24,40

B)
21,35

C)
36,60

D)
48,80


Correct Answer :

48,80


Explanation :

Suppose two numbers are 3x and 5x.
Then, 3x * 5x = HCF * LCM
15x2 = 16 * 240
x2 = 256
x = 16

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?


दो नंबरों के महत्तम समापवर्तक(HCF) और लघुतम समापवतर्क(LCM) क्रमश: 66 और 384 है। यदि पहला नंबर 2 से विभाजित करने पर 66 प्राप्त होता है।तो दूसरा नंबर है?

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?


दो संख्याओं का लघुतम समापवतर्क(LCM) 280 है और संख्याओं का अनुपात 7: 8 है। तो संख्याएं क्या हैं?

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?


105, 150 और 210 का महत्तम समापवर्तक(HCF) x है, 126, 396 और 1080 का महत्तम समापवर्तक(HCF) y है ,और 440, 180 और 280 का महत्तम समापवर्तक(HCF) z है।तो निम्नलिखित में से कौन सा सबसे बड़ा है?

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?


5 घंटे एक साथ बजना शुरू करते हैं और क्रमश: 6, 7, 8, 9 और 12 सेकंड के अंतराल पर बजते हैं । कितने सेकंड के बाद वे फिर एक साथ बजेंगे ?

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, B और C एक ही समय एक वृतकार स्टेडियम में एक ही बिंदु से एक ही दिशा में भागना शुरू करते हैं । A एक चक्कर 252 सेकंड में पूरा कर लेता है, B 308 सेकंड में, और C 198 सेकंड में । वे आरंभिक बिंदु पर कितने समय बाद फिर मिलेंगे?

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?


दो संख्याओं का लघुत्तम समापवर्तक 520 है तथा उनका महत्तम समापवर्तक 4 है । यदि उनमें एक संख्या 52 हो, तो दूसरी संख्या क्या होगी?

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?


दो प्राकृतिक संख्याओं का HCF और LCM क्रमशः 12 और 72 है। दोनों संख्याओं का अंतर क्या होगा यदि इनमें से एक संख्या 24 है?

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?


दो नंबर 63 और 77 हैं, महत्तम समापवर्तक (HCF) 7 है, लघुत्तम समापवर्तक LCM ज्ञात करे ?

A)

668


B)

693


C)

674


D)

680



Correct Answer :

693


Explanation :

LCM = 63 * 77 / 7 = 693

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