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

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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

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Find the largest five digits number that is divisible by 7, 10, 15, 21 and 25?

A)
98700

B)
98950

C)
99750

D)
None of these


Correct Answer :

99750


Explanation :

The least number which is exactly divisible by 7, 10, 15, 21 and 25 is their L.C.M, i.e.
L.C.M of 7, 10, 15, 21 and 25 =1050

The Largest number of five digits is 99999.
Required number must be divisible by L.C.M of 7, 10, 15, 21 and 25 i.e. 1050
On dividing 99999 by 1050 get 249 as remainder.
So required number is = (99999-249) = 99750.

How many possible pairs of numbers exist whose product is 5400 and HCF is 30?

A)
1

B)
2

C)
3

D)
4


Correct Answer :

2


Explanation :

H.C.F of numbers is 30 So required numbers should be multiple of 30.
lets the numbers are 30a and 30b ,there the product of the numbers = 5400
Then,
30a * 30b = 5400 <=> ab = 6

the co-primes or possible pairs of product 6 either (1, 6) and (2,3), or (6,1) and (3, 2)
that means
a*b=6
30a*30b = 5400

30*180 = (30,180) = 5400 (there (1, 6) a=1 , b=6)
60*90 = (60,90) = 5400 (there (2, 3) a=2 , b=3)

thus,two numbers of pairs are possible whose product is 5400 and H.C.F. is 30.

The HCF and LCM of two numbers are 8 and 48 respectively. If one of the numbers is 24, then the other number is?

A)
48

B)
36

C)
24

D)
16


Correct Answer :

16


Explanation :

lets other number is Z
as per rule, Product of two numbers =Product of their H.C.F. and L.C.M
So Z*24=8*48
Z=384/24 => 16

Three bells toll at interval of 36 seconds, 40 seconds and 48 seconds respectively. They started ringing together at particular time. They next toll together after?

A)
12 min

B)
6 min

C)
24 min

D)
18 min


Correct Answer :

12 min


Explanation :

Least common multiples (LCM) of Interval of bells toll:
= (36 to 40 to 48)/2
= (18 to 20 to 24)/2
= (9 to 10 to 12)/2
= (9 to 5 to 6)/3
= (3 to 5 to 2)

So,They will start ringing together again after: = (2 * 2 * 2 * 3 * 3 * 5 * 2) sec = 720 sec
Thus , next toll together after 720 sec i.e. 12 mins

Three wheels can complete 60, 36, 24 revolutions per minute respectively. There is red mark on each wheel that touches the ground at time zero. After how much time, all these spots will simultaneously touch the ground again?

A)
2.5 second

B)
1.6 second

C)
5 second

D)
7.5 second


Correct Answer :

5 second


Explanation :

The first wheel spins at 60 rpm which means that it completes 60/60 = 1 revolution every second.
The second wheel spins at 36 rpm. So it completes 36/60 = 0.6 of a revolution every second
The third wheel spins at 24 rpm. So it completes 24/60 = 0.4 of a revolution every second.

So we have the values: 1, 0.6, 0.4
If we wait 10 seconds, then we multiply each value by 10 to get: 10, 6, 4
Now we can divide by the GCF 2 to get 5, 3, 2

This means that it will take 5 seconds for the spots to line up again (since the first number corresponds to the amount of time that has gone by in seconds)

Find the HCF of the numbers a and b, where a = 25*32*76*114 and b = 23*34*56*11*133 ?

A)
396

B)
408

C)
792

D)
1584


Correct Answer :

792


Explanation :

HCF is the product of all common prime factors using the least power of each common prime factor
HCF = 23 x 32 x 11 = 792

What is the least number of that is exactly divisible by 4, 12, 15, and 18?

A)
120

B)
108

C)
180

D)
240


Correct Answer :

180


Explanation :

The least number which is exactly divisible by is their LCM of (4, 12, 15, and 18)
=4,12,15,18|2
=2,6,15,9|3
=2,2,5,3|2
=1,1,5,3
LCM=2*3*2*1*5*3=180

The HCF of 2 numbers is 11 and LCM is 693.If one of numbers is 77.find the other number ?

A)
99

B)
198

C)
66

D)
143


Correct Answer :

99


Explanation :

Product of two numbers = Product of their HCF and LCM
77 x a = 11 x 693
Other number a = 11 x 693 / 77 =99.

The largest number , which exactly divides 210, 315, 147 and 168 is ?

A)
3

B)
7

C)
21

D)
4410


Correct Answer :

21


Explanation :

The largest number is the H.C.F. of 210, 315, 147, and 168, which is 21.

The H.C.F and L.C.M of two number are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is ?

A)
33

B)
66

C)
132

D)
264


Correct Answer :

132


Explanation :

Product of two numbers = Product of their HCF and LCM.

First number = 2 x 44 = 88
Second number = (LCM x HCF ) / First number
So, Second number = 44 x 264 / 88 = 132.

Find the HCF of 22 * 32, 2 * 34 * 7 ?

A)
128

B)
126

C)
146

D)
434


Correct Answer :

126


Explanation :

22 * 32 =>2*2*3*3
2 * 34 * 7=>2*3*3*3*3*7

HCF is the product of all common prime factors using the least power of each common prime factor.
So we got 2*3*3*7 = 126

Find the HCF of 54, 288 and 360 ?

A)
18

B)
36

C)
54

D)
72


Correct Answer :

18


Explanation :

Let’s solve this question by factorization method.
54 =2 * 33
288 = 25 * 32
360 = 23 * 32 * 5
So HCF is the product of all common prime factors using the least power of each common prime factor in all three, i.e. 2 * 3² =18

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)?

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 ?

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?

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 ?

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

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