**Question 1: ** Find the HCF by long division method of two no’s the sequence of quotient from top to bottom is 9, 8, 5 and the last divisor is 16. Find the two no’s.

**Solution: ** Start with the divisor and last quotient.

Divisor x quotient + remainder = Dividend

16 x 5 + 0 = 80

80 x 8 + 16 = 656

**656** x 9 + 80 = **5984**

Hence, two numbers are** 656 and 5984.**

**Question 2: ** The LCM and HCF of two numbers is 210 and 5. Find the possible number of pairs.

**Solution: ** HCF = 5 so it should be multiple of both numbers.

So both numbers 5x : 5y

LCM = 5 * x * y = 210

x * y = 42

{1 x 42}, { 2 x 21}, {3 x 14}, { 6 x 7 } .

**Four pairs are possible**.

**Question 3: ** The sum of two numbers is 132 and their LCM is 216. Find both the numbers.

**Solution: **

**Note: ** HCF of Sum & LCM is also same as actual HCF of two numbers.

Factorize both 132 and 216 and find the HCF.

132= 2^{2} x 3 x 11

216= 2^{3}x 3^{3}

HCF= 2^{2} x 3 =12

Now, 12x + 12y = 132

x + y = 11

And 12 * x * y = 216

x * y = 18

Solve for x and y, we get y = 9 and x = 2. Hence both numbers are 12*2 = **24** and 12*9 = **108**

**Question 4: ** The LCM of two numbers is 15 times of HCF. The sum of HCF and LCM is 480. If both number are smaller than LCM. Find both the numbers.

**Solution: ** LCM = 15 * HCF

We know that

LCM + HCF = 480

16 * HCF = 480

HCF = 30

Then LCM = 450

LCM = 15 HCF

30 * x * y = 15 * 30

x * y = 15

Factors are {1 x 15} and { 3 x 5}

Both numbers less than LCM so take {3 x 5}

Hence numbers are 3 * 30 = **90** and 5 * 30 = **150**

**Question 5: ** Find the least perfect square number which when divided by 4, 6, 7, 9 gives remainder zero.

**Solution: ** Find the LCM for 4, 6, 7, 9

LCM= 2^{2} * 3^{2} * 7 = 252

To become perfect square all factors should be in power of 2.

So, multiply it by 7

LCM = 2^{2} * 3^{2} * 7^{2} = 1764

And it is perfect square of **42**.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.

## Recommended Posts:

- LCM and HCF
- TCS Coding Practice Question | HCF or GCD of 2 Numbers
- TCS Coding Practice Question | LCM of 2 Numbers
- Problem on Pipes and Cisterns
- Problem on Time Speed and Distance
- Problem on Trains, Boat and streams
- Problem on Numbers
- Work and Wages
- Pipes and Cisterns
- Trains, Boats and Streams
- Ratio Proportion and Partnership
- Mixture and Alligation
- Profit and Loss
- Trigonometry & Height and Distances
- Permutation and Combination
- Assumptions and Conclusions, Courses of Action
- Error Detection and Correction
- Permutation and Combination | Set-2
- Trigonometry & Height and Distances | Set-2
- Cvent Interview Experience (On campus for Internship and Full Time)

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.