Problems on HCF and LCM - Aptitude Questions Part 2

6. A 4 digit number which when divided by 12, 16 and 18 gives out a common remainder i.e. 21. Find the smallest/ least such number.

a. 36
b. 133
c. 144
d. 1461

Answer: d. 1461

Explanation:

Here least possible 4 digit number is needed that means we need the LCM

We must first find LCM of 12, 16, 18 and 20
--------------------------------------------------------
2           12           16           18           20
--------------------------------------------------------
3           6             8              9             10
2           2             8              3             10
             1             4              3              5
--------------------------------------------------------
∴ LCM = 2 x 3 x 2 x 1 x 4 x 3 x 5 = 720

Now this is a 3 digit number.
If we multiply it by 2 we get (720 x 2) = 1440 → (4 digit number)
But 1440 is divisible by 12, 16, 18 and 20
We must have 21 as remainder, as per given condition.
So, Number = 1440 + 21 = 1461


7. The two given numbers A and B are in the ratio 5:6 such that their LCM is 480. Find their HCF.

a. 12
b. 16
c. 96
d. 240

Answer: b. 16

Explanation:

Tip:
If A and B are two numbers,
A x B = HCF of A and B x LCM of A and B


Let K be common factor. So 2 numbers are 5K and 6K
Also K is the greatest common factor (HCF) as 5 and 6 have no other common factor
∴ 5K x 6K = 480 x K
K = 16 = HCF


8. The sum of two given numbers P and Q is 56. Their LCM and HCF is 96 and 8 respectively.
Find the sum of1+1.
PQ

a.1
96
b.1
56
c.7
96
d.1
8

Answer: c.7
96

Explanation:

Tip:
If A and B are two numbers,
A x B = HCF of A and B x LCM of A and B


Let numbers be P and Q
Also, P + Q = 56 and PQ = HCF x LCM = 8 x 96
1+1=P + Q=56=7
PQPQ8 x 9696


9. Find the largest number which when divides 47, 35 and 27 leaves the same remainder. Also find the value of the remainder.

a. 3, 4
b. 4, 3
c. 1, 9
d. 9, 1

Answer: b. 4, 3

Explanation:

What to do when we don't know the remainder and the largest number which divides?
In such cases subtract the 3 numbers from each other
47 - 35 = 12
35 - 27 = 8
27 - 47 = -20 (Ignore minus sign)
Largest number is needed that means we need HCF of 12, 8 and 20
------------------------------------
4           12           8           20
------------------------------------
             3             2            5
------------------------------------
Cannot divide further
∴ HCF = 4 = Largest number that can divide leaving common remainder

47= 113
44
∴ Common remainder = 3


10. Find the largest scale size to measure accurately, the three equilateral triangles with sides measuring 76 cm, 114 cm and 152 cm.

a. 19 cm
b. 21 cm
c. 38 cm
d. None of the above

Answer: c. 38 cm

Explanation:

Here the answer is HCF of 114, 76 and 152
------------------------------------------
2           76           114           152
------------------------------------------
19         38           57             76
             1             3               2
------------------------------------------
∴ HCF = 2 x 19 = 38 = Maximum scale size needed to measure all 3 exactly

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