LCM and HCF Test

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LCM and HCF Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

The smallest positive number which leaves a remainder of 1 when it is divided by 3, 4, 5 or 7 is

A
85

B
106

C
141

D
421

Solution

The smallest positive number which leaves a remainder of 1 when it is divided by 3, 4, 5 or 7 is

LCM of (3,4,5,7 ) + 1

Required no. = 420 + 1 = 421
Question 2
1 / -0

What is the least number by which 825 must be multiplied in order to produce a multiple of 715?

A
13

B
11

C
9

D
8

Solution

825 = 3 × 5 × 5 × 11
715 = 5 × 11 × 13.
In 825, 13 is missing. Rest all the factors of 715 are present in 825.
Question 3
1 / -0

HCF of 4 × 27 × 3125; 8 × 9 × 25 × 7 and 16 × 81 × 5 × 11 × 49 is

A
180

B
360

C
540

D
260

Solution

4 × 27 × 3125 = 4 × 9 × 3 × 5 × 5 × 125
8 × 9 × 25 × 7 = 4 × 2 × 9 × 5 × 5 × 7

16 × 81 × 5 × 11 × 49 = 4 × 4 × 9 × 9 × 5 × 11 × 7 × 7
Common factors with least powers = 4 × 9 × 5 = 180.
Question 4
1 / -0

What is the smallest sum of money which contains an integral number of $2.50, $20, $1.20 and $7.50 each?

A
$60

B
$80

C
$90

D
$100

Solution

The smallest sum of money that contains an integral number of $2.50, $20, $1.20 and $7.50 is the money the numerical value of which is equivalent to the LCM of 2.50, 20,
1.20 and 7.50
2.50 = 25/ 10 = 5/2
1.20 = 12/10 = 6/5
7.50 = 75/10 = 15/2

Thus, we need to evaluate the LCM of 5/2, 20/1, 6/5 and 15/2 = LCM of (5, 20, 6, 15)/(HCF of 2, 1 , 5) = 60/1

Thus the smallest sum of money is $ 60
Question 5
1 / -0

Find the least square number which is exactly divisible by 4, 5, 6, 15 and 18.

A
900

B
1200

C
1500

D
1600

Solution

LCM of 4, 5, 6, 15, and 18 = 180

So, Required answer must be the multiple of 180.

180 can be written as = 2 x 2 x 3 x 3 x 5 Only 5 is not in pair,
We need to multiply by 5 for perfect square.
180 x 5 = 900

So, the least number be 900.
Question 6
1 / -0

From 3 drums of milk, 27 L, 33 L and 45 L are to be drawn. To do it in the minimum number of repetitions, the capacity of the measuring can should be

A
27 L

B
11 L

C
9 L

D
3 L

Solution

To find the required answer, we need to find the HCF of these numbers (27, 33 and 45). The HCF is the required answer.
27 = 3³
33 = 3 × 11
45 = 3² × 5
HCF = 3
Question 7
1 / -0

Two cyclists are preparing for the Olympics. The first cyclist takes 10 minutes to cover one full round, whereas the second cyclist takes 9 minutes. Find the time when they will both be together at the starting point, if they both start simultaneously.

A
90 minutes

B
95 minutes

C
98 minutes

D
99 minutes

Solution

This might deceptively seem to be a problem on Time, Speed and Distance. But the logic is based on the concept of LCM.

The first cyclist will be at the starting point at every multiple of 10 minutes. The second will be at the starting point at every multiple of 9 minutes. So, they will be together at the starting point for the first time, after the LCM of 10 and 9 = 90 minutes.

In this problem, in 90 minutes, the first cyclist will complete 9 rounds and the second will complete 10 rounds. So, the second cyclist has taken a lead of 1 full round over the first. It coincidentally happens that they will be meeting for the first time at the starting point after their start.
Question 8
1 / -0

A heap of coconuts is divided into groups of 2, 3 or 5 and each time, no coconut is left over. Find the least number of coconuts in the heap.

A
1

B
10

C
15

D
30

Solution

Let X be the number of coconuts desired. X must be a common multiple of 2, 3 and 5, otherwise some coconuts will be left over. Further, the number X must be the least possible number. So, X has to be the LCM of 2, 3, 5, which is 30. So, the least number of coconuts in the heap is 30.
Question 9
1 / -0

An electric wire is sold only in multiples of 1 m and a customer requires several lengths of wire, each 85 cm long. To avoid any wastage and to minimise labour, he should purchase a minimum length of

A
1.7 m

B
8.5 m

C
17 m

D
85 m

Solution

Take the LCM of 100 cm and 85 cm = 1700 cm = 17 m.

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Re-Attempt Weekly Quiz Competition

LCM and HCF Test - 1

Result

LCM and HCF Test - 1

Score

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Rank

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SHARING IS CARING

Question 1

85

106

141

421

Solution

Question 2

13

11

9

8

Solution

Question 3

180

360

540

260

Solution

Question 4

$60

$80

$90

$100

Solution

Question 5

900

1200

1500

1600

Solution

Question 6

27 L

11 L

9 L

3 L

Solution

Question 7

90 minutes

95 minutes

98 minutes

99 minutes

Solution

Question 8

1

10

15

30

Solution

Question 9

1.7 m

8.5 m

17 m

85 m

Solution

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