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# Problem on LCM and HCF

## Best explanation to understand and solve the problems on LCM and HCF.

This section is the aptitude test for problems on LCM and HCF. LCM and HCF problems will be asked in most of the aptitude tests conducted for  various entrance exams and certificate exams.

Through our test , learn the basic concepts and strategies to solve LCM and HCF problems. Try to find the answers for our multiple choice questions and increase you ability in solving problems fast.

### LCM - LEAST COMMON MULTIPLE

LCM stands for Least Common Multiple or Lowest Common Multiple.

A multiple is a number that you will get when you multiply a number with a whole number. A factor is a number with which you can multiply another number to get any positive integer.

Example : 8 is the factor for 8, 16, 24, 32, 40, etc. Here 8 is multiplied with various numbers like 1, 2, 3, 4, 5 to get a positive integer.

Finding out the lowest common factor for two or more numbers is called LCM.

#### Needs Of LCM

When you want to add , subtract or compare two fractions, you need to know the common factor for both the denominators.

If the denominator of the given two numbers are not the same, it will be difficult to find the addition or subtraction of the factors.

So to find a common factor for the denominator of two fractions, we use the method of LCM.

#### How to Find LCM?

One easy way to find the least common multiple of any two numbers is that, first to list the prime factors of each number.

After listing the prime factors, multiply each factor till the greatest number of times it occurs for both the number.

If the same factor occurs more than once for both the numbers, multiply the factors that occurred the most and find the LCM.

After finding the LCM , don’t forget to check whether the LCM number can be divided by both the numbers given in the question.

### HCF - HIGHEST COMMON FACTOR

HCF stands for Highest Common Factor. This is the largest positive integer that divides two or more integers without any remainder.

It is also called as Greatest Common Divisor or Greatest Common Factor (GCF).

Common factor is nothing but two or more numbers have the same number as the factor.

Example : 8 and 16 have the same common factor of 1, 2, and 4.

#### Needs Of HCF

HCF is very useful for reducing the fraction to the most simplest form.

If we have a set of numbers and if we need to find one number that can be a factor of all these numbers,  then the particular factor is the HCF of the set of numbers.

FOR EXAMPLE:  21, 28, 14 are the set of numbers. The HCF of these numbers is 7 because this the highest common factor and also when divided they bring no reminder.

#### How to Find HCF?

HCF of two or more numbers can be found by three methods. They are as follows

1. Factorization method
2. Prime factorization method
3. Division method.

Factorization Method: In this method we write down the factors of the given two or more numbers and find the common factor that can be divisible by both the numbers. This is one of the easiest methods to find HCF.

Prime Factorization Method:  In this method a factor tree diagram is drawn to find the factors for the given numbers. The method will continue till all the factors become prime numbers.

Division Method: In this method factors of the numbers are derived through long division. This is a kind of complex method to find the HCF. Most probably you can find the HCF using the first two methods which are easy.

### Difference And Relationship Between LCM and HCF

LCM is the smallest common multiple of given two or more numbers. But  HCF is the largest common factor of given two or more numbers.

There is a special relationship between LCM and HCF. the product of LCM and HCF are same as the products of the given two numbers. But this may vary if there are more than two numbers.

### Important Points To Be Remembered

1) H.C.F. and L.C.M. of Fractions

H.C.F. =H.C.F. of Numerator/L.C.M. of  Denominator

2) Product of two numbers = Product of their H.C.F. and L.C.M.

1.

What would be the HCF of 6 and 12 ?

2.

Which smallest integer when increase by 7 the integer thus formed will be divided by 8 , 11 and 24 ?

3.

Which littlest whole square integer when divided by 4 , 5 , 6 , 15 and 18 remain no left over ?

4.

What will be the H.C.F of 10 and 30 ?

5.

In the place of (*) which littlest figure are to be place so that the integer 5718*7 will be divided by 11.

6.

The average of two numbers is 2800 . and their H.C.F is 14. what is the greater number ?

7.

By the help of which biggest integer 84, 182 and 278 be divided so that there remain same left over in each division.

8.

Find the H.C.F. of the polynomials

2x2 - 8 and 5x2 -- 20x + 20.

9.

The H.C.F of two numbers is 3120. there H.C.F is 12 ? what is the greater number in that ?

10.

With 2497 which littlest integer are to be add so that when divide by integer 3 , 4 , 5 and 6 there will be no left over.

11.

What is the H.C.F. of the polynomials

(2x-3)2(x2+x-2)

4x2-x-18

2x2--9x+9.

12.

What is the H.C.F. of the polynomials x2 - 9 and x3 + 27 ?

13.

Find the least number which is exactly divisible by 18, 30, 45, 63.

14.

The HCF and the LCM of two numbers are 23 and 644 respectively. If one of the numbers is 92, find the other number.

15.

The L.C.M of two numbers is 1208. and their H.C.F is 4 / what is the greater number ?

16.

The L.C.M of two numbers is 576 and H.C. F is 12. What is the greater number ?

17.

The L.C.M of two numbers is 1100, their H.C.F is 4 . what is the greater number ?

18.

The L.C.M of two numbers is 1600. and their H.C.F is 8.Find the Greater number ?

19.

What is the LCM of first five even numbers?

20.

The LCM of two numbers is 1089. Their H.C.F is 9 ?

21.

If the G.C.F and L.C.M of two integers v and w are 6 and 210 respectively and if v + w = 36 , find {(1/v + (1/w)}

22.

Calculate the G.C.F of 3.5 , 11.2 and 14.

23.

The L.C.M of two numbers is 1140. Their H.C.F is 12 ? What is the greater number ?

24.

What is the HCF of the highest 3 digits and smallest 3 digits number ?

25.

What is the littlest integer of 5 figures which when divided by 16 , 32 , 48 and 56 gives a whole number answer.

26.

Which bigger numeral will divide 73 , 121 and 213 numerals so that after every division there will be same left over?

27.

Find g(x) if f(x)= 5x^2+4 and f(g(3))= 84