# LCM and HCF Questions and Answers

## HCF and LCM Questions with Solutions

LCM and HCF Questions and Answers are provided on this page for students to practice and get an idea how this topic is asked in the exam.

### HCF in case of only two numbers:

• Suppose the question asks to calculate the HCF of any two numbers. Then Divide the larger number by the smaller one.
• Now divide the divisor by the remainder.
• Keep dividing the preceding divisor with the remainder until a Zero remainder is obtained.
• The last divisor obtained will be the HCF of those two given number.

### HCF in case of more than two numbers:

• The HCF of these two numbers and the third number will be the HCF of all three numbers and so forth.
• Choose any two numbers and find their HCF by applying the above-mentioned method.

### The rule for Solving HCF and LCM Questions and Answers:

•  Calculate the multiples or the factors of the larger number until one of them is also a multiple of the smaller number.
• Then multiply all these factors, and the resultant will be the LCM of the given numbers.

## Practice LCM and HCF Questions and Answers

1. Find the L.C.M of 15, 30, 45

90

90

83.59%

95

95

4.3%

92

92

1.71%

None of the above

None of the above

10.41%

2 | 15, 30, 45
3 | 15, 15, 45
3 | 5, 5, 15
5 | 5, 5, 5
| 1, 1, 1

L.C.M = 2*3*3*5 = 90

2. The given ratio of two numbers is 3:2. If the L.C.M of them is 30, then calculate their sum.

34

34

9.61%

25

25

75.77%

55

55

5.9%

None of the above

None of the above

8.72%

Given:

Ratio of the two numbers = 3: 2

LCM of two numbers = 30

To find: Sum of the two numbers

The formula used: Product of two numbers = LCM × HCF

Solution:

Let the numbers be 3x and 2x

Product of two numbers = LCM × HCF

The HCF of two numbers will be x as the numbers are in ratio due to which it c an be conclude that their will be a HCF factor of x also.

The two numbers are 3x,2x

Product of two numbers = LCM × HCF

(3x )(2x) = 30 (x)

6x2 = 30x

6x = 30

x = 30/6

x = 5

The first number is 3x

3x = 3(5)

= 15

The first number is 15

The second number is 2x

2x = 2(5)

=10

The second number is 10

Therefore the two numbers are 15,10

The sum of two numbers = 15 + 10

= 25

The ratio of two numbers is 3 ratio 2 and the lcm of them is 30 then  the sum​ of the numbers is 25

3. Find the L.C.M of 25, 35, and 55

1900

1900

4.77%

1990

1990

5.46%

1925

1925

83.08%

None of the above

None of the above

6.69%

5 | 25, 35, 55
5 | 5, 7, 11
7 | 1, 7, 11
11 | 1, 1, 11
| 1, 1, 1

L.C.M = 5*5*7*11 = 1925

4. Calculate the HCF of 22 and 33

11

11

92.97%

12

12

2.65%

15

15

1.6%

None of the above

None of the above

2.78%

22 = 2*11

33 = 3*11

So the HCF will be 11

5. If 20 is the HCF of two particular numbers and the other two factors of their LCM are 10 and 12, find the larger number?

220

220

13.38%

210

210

9.82%

240

240

74.25%

None of the above

None of the above

2.54%

20* 10 = 200

20*12 = 240

So the larger number will be 240

HCF of two numbers is the number that is a common factor for both numbers given

Here 20 is the common factor.

Other than this common factor, we also will have the product of uncommon factors for the two numbers (10 and 12 here).

The first number = 20*10 = 200

and second number = 20 × 12 = 240

The greatest of two numbers is definitely 20 × 12 = 240

6. The HCF  of three specific numbers 6, 12, and 18 is 24 , find the LCM?

55

55

4.02%

54

54

73.92%

67

67

3.81%

None of the above

None of the above

18.25%

(6*12*18)/24

The next number will be = 54

7. The two specific numbers are in the ratio 6:7, if the HCF of the given numbers is 30, what will be the numbers?

160, 180

160, 180

6.04%

180, 210

180, 210

87.81%

200,160

200,160

3.6%

None of the above

None of the above

2.55%

Let the numbers be 6y and 7y

HCF = 30

The numbers will be 6*30 = 180

And 7*30 = 210

8. Determine the largest length of the tape, which can measure tape of 5 cm, 7cm, and 13 cm?

1

1

57.45%

7

7

3.76%

13

13

31.37%

None of the above

None of the above

7.42%

As all these numbers have no factors and are considered as prime numbers so their HCF will be 1.

9. The HCF of two numbers is 45, and their LCM is 90, if one specific number is 9, find the other number.

450

450

89.38%

435

435

6.16%

426

426

2.37%

None of the above

None of the above

2.09%

HCF * LCM = Products of Numbers

45 * 90 = 9 * x

Another number will be = (45*90)/9 = 450

10. Street lamps start at the interval of 5, 10, 15, 20, and 25 seconds, calculate the number in which the street lamps began together in 40 minutes.

9 times

9 times

22.28%

10 times

10 times

14.37%

8 times

8 times

53.76%

None of the above

None of the above

9.58%

we need to calculate the number of occurrences when the time intervals (5 seconds, 10 seconds, 15 seconds, 20 seconds, and 25 seconds) align perfectly with each other within the 40-minute interval.

First, let's convert 40 minutes to seconds:

40 minutes * 60 seconds/minute = 2400 seconds

Now, let's find the least common multiple (LCM) of the given time intervals (5, 10, 15, 20, 25 seconds) to determine when the street lamps will start together. The LCM of these intervals is 300 seconds.

Next, we'll divide the total interval time (2400 seconds) by the LCM (300 seconds):

2400 seconds / 300 seconds = 8

So, the street lamps will start together 8 times within a 40-minute interval.

Therefore, the number of times the street lamps began together in 40 minutes is 8.

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