# Word problems on H.C.F. and L.C.M.

Here we will get the idea how to solve the word problems on H.C.F and L.C.M.

1. Find the smallest number which on adding 19 to it is exactly divisible by 28, 36 and 45.

First we find the least common multiple (L.C.M.) of 28, 36 and 45.

Therefore, least common multiple (L.C.M.) of 28, 36 and 45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260

Therefore, the required number = 1260 - 19 = 1241

2. Find the number which divides 167 and 95 leaving 5 as remainder.

The number divides 167 and leaves 5 as remainder

Therefore, the number divides 167 - 5 = 162 exactly

The number also divides 95 leaving 5 as remainder

Therefore, the number divides 95 - 5 = 90 exactly

Now we have to find highest common factor (H.C.F.) of 162 and 90

Highest common factor (H.C.F.) of 90 and 162 = 18

Therefore, 18 is the required number.

3. Find the largest number that divides 92 and 74 leaving 2 as remainder.

The number divides 92 and leaves 2 as remainder

Therefore, the number divides 92 - 2 = 90 exactly

The number also divides 74 leaving 2 as remainder

Therefore, the number divides 74 - 2 = 72 exactly

Now we have to find highest common factor (H.C.F.) of 90 and 72

Highest common factor (H.C.F.) of 90 and 72 = 18

Therefore, 18 is the required number.

4. Nairitee saves $8.85 daily. Find the least number of days in which she will be able to save an exact number of dollars. Solution: The number of dollars will always be a multiple of 100 cents, like: 2 = 2 × 100 cents = 200 cents 5 = 5 × 100 cents = 500 cents We know that$8.85 = 885 cents.

Hence, saved money will be a multiple of 885 cents.

Now, the LCM of 100 and 885 is as follows:

5  |  100,    885

20,    177

LCM of 100 and 885 = 17700

So, Nairitee saves 17700 cents.

Therefore, the required number of days = 17700/885 = 20 days.

5. Find the least number which, when divided by 12, 22 and 26, leaves a remainder of 7 in each case.

Solution:

The least number which is exactly divisible by 12, 22 and 26 is the LCM of these numbers.

Let us find the LCM of 12, 22 and 26.

Prime factorization of the numbers 12, 22 and 26.

12 = 2 × 2 × 3

22 = 2 × 11

26 = 2 × 13

Therefore, the LCM of (12, 22, 26) = 2 × 2 × 3 × 11 × 13 = 1716

But, the required number is a number that leaves a remainder of 7 in each case.

That means the required number is 7 more than the LCM.

Required number 1716 + 7 = 1723.

6. Find the greatest 4-digit number which when divided by 12, 18 and 24 leaves a remainder of 5 in each case.

Solution:

First, we find the LCM of 12, 18 and 24 as shown below.

Prime factorization of the numbers 12, 18 and 24

12 = 2 × 2 × 3

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

Therefore, LCM of 12, 18 and 24 = 2 × 2 × 2 × 3 × 3 = 72

Hence, 72 is the least number divisible by 12, 18 and 24.

Now, the greatest 4-digit number is 9999.

So, we have to find the greatest multiple of 72 which is just less than 9999.

To find the number, we have to divide 9999 by 72.

Now, 9999 - 63= 9936, which is exactly divisible by 72 (i.e., divisible by 12, 18 and 24 also).

But, the required number leaves a remainder 5 in each case.

Hence, the required number = 9936 + 5 = 9941.

7. Find the largest number that will divide 251, 361 and 487 leaving remainders 3, 5 and 7 respectively.

Solution:

We find that

251 - 3 = 248

361 - 5 = 356

487 - 7 = 480

Now, the numbers exactly divisible are 248, 356 and 480.

Let us first find the HCF of 248 and 356 as shown below.

Thus, the HCF of 248 and 356 = 4.

Now, we find the HCF of 4 and 480.

The HCF of 4 and 480 = 4

Thus, the HCF of 248, 356 and 480 = 4.

Hence, the required largest number = 4.

8.
Find the number nearest to hundred thousand (one-lakh) but must greater than hundred thousand (one-lakh) which is exactly divisible by 4, 12 and 18.

Solution:

First, we find the LCM of 4, 12 and 18.

Prime factorization of the numbers 4, 12 and 18.

4 = 2 × 2

12 = 2 × 2 × 3

18 = 2 × 3 × 3

Therefore, the LCM of 4, 12 and 18 = 2 × 2 × 3 × 3 = 36

Now, we divide 100000 by 36 as shown below.

Therefore, the number nearest to 100000 and divisible by 36 (i.e. divisible by 4, 12, and 18), is equal to (100000 - 28) = 99972.

But, since 99972 is less than 100000, the next number which would be divisible by 36 (i.e. divisible by 4, 12, and 18), will be 99972 + 36 = 100008 which is greater than 100000.

Therefore the the required number = 100800.

## You might like these

• ### Highest Common Factor |Find the Highest Common Factor (H.C.F)|Examples

Highest common factor (H.C.F) of two or more numbers is the greatest number which divides each of them exactly. Now we will learn about the method of finding highest common factor (H.C.F). Steps 1: Find all the factors of each given number. Step 2: Find common factors of the

• ### Prime Factorisation |Complete Factorisation |Tree Factorisation Method

Prime factorisation or complete factorisation of the given number is to express a given number as a product of prime factor. When a number is expressed as the product of its prime factors, it is called prime factorization. For example, 6 = 2 × 3. So 2 and 3 are prime factors

• ### Multiples and Factors | Infinite Factors | Multiply Counting Numbers

We will discuss here about multiples and factors and how they are related to each other. Factors of a number are those numbers which can divide the number exactly. For example, 1, 2, 3 and 6 are

• ### Divisible by 3 | Test of Divisibility by 3 |Rules of Divisibility by 3

A number is divisible by 3, if the sum of its all digits is a multiple of 3 or divisibility by 3. Consider the following numbers to find whether the numbers are divisible or not divisible by 3: (i) 54 Sum of all the digits of 54 = 5 + 4 = 9, which is divisible by 3.

• ### Divisible by 4 | Test of Divisibility by 4 |Rules of Divisibility by 4

A number is divisible by 4 if the number is formed by its digits in ten’s place and unit’s place (i.e. the last two digits on its extreme right side) is divisible by 4. Consider the following numbers which are divisible by 4 or which are divisible by 4, using the test of

• ### Divisible by 5 | Test of divisibility by 5| Rules of Divisibility by 5

Divisible by 5 is discussed below: A number is divisible by 5 if its units place is 0 or 5. Consider the following numbers which are divisible by 5, using the test of divisibility by

• ### Divisible by 6 | Test of Divisibility by 6| Rules of Divisibility by 6

Divisible by 6 is discussed below: A number is divisible by 6 if it is divisible by 2 and 3 both. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42

• ### Divisible by 8 | Test of Divisibility by 8 |Rules of Divisibility by 8

Divisible by 8 is discussed below: A number is divisible by 8 if the numbers formed by the last three digits is divisible by 8. Consider the following numbers which are divisible by 8

• ### Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7

Divisible by 7 is discussed below: We need to double the last digit of the number and then subtract it from the remaining number. If the result is divisible by 7, then the original number will also be

• ### Divisible by 9 | Test of Divisibility by 9 |Rules of Divisibility by 9

A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9. Consider the following numbers which are divisible by 9, using the test of divisibility by 9:

• ### Divisible by 10|Test of Divisibility by 10|Rules of Divisibility by 10

Divisible by 10 is discussed below. A number is divisible by 10 if it has zero (0) in its units place. Consider the following numbers which are divisible by 10, using the test of divisibility by 10:

• ### Least Common Multiple |Lowest Common Multiple|Smallest Common Multiple

The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is the smallest of all common multiples.

• ### Multiples | Multiples of a Number |Common Multiple|First Ten Multiples

What are multiples? ‘The product obtained on multiplying two or more whole numbers is called a multiple of that number or the numbers being multiplied.’ We know that when two numbers are multiplied the result is called the product or the multiple of given numbers.

• ### Even and Odd Numbers Between 1 and 100 | Even and Odd Numbers|Examples

All the even and odd numbers between 1 and 100 are discussed here. What are the even numbers from 1 to 100? The even numbers from 1 to 100 are:

• ### Prime and Composite Numbers | Prime Numbers | Composite Numbers

What are the prime and composite numbers? Prime numbers are those numbers which have only two factors 1 and the number itself. Composite numbers are those numbers which have more than two factors.

To Find Lowest Common Multiple by using Division Method

Examples to find Least Common Multiple of three numbers by using Division Method

Worksheet on H.C.F. and L.C.M.

Word problems on H.C.F. and L.C.M.

Worksheet on word problems on H.C.F. and L.C.M.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Constructing a Line Segment |Construction of Line Segment|Constructing

Aug 14, 24 09:52 AM

We will discuss here about constructing a line segment. We know how to draw a line segment of a certain length. Suppose we want to draw a line segment of 4.5 cm length.

2. ### Construction of Perpendicular Lines by Using a Protractor, Set-square

Aug 14, 24 02:39 AM

Construction of perpendicular lines by using a protractor is discussed here. To construct a perpendicular to a given line l at a given point A on it, we need to follow the given procedure

3. ### Construction of a Circle | Working Rules | Step-by-step Explanation |

Aug 13, 24 01:27 AM

Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

4. ### Practical Geometry | Ruler | Set-Squares | Protractor |Compass|Divider

Aug 12, 24 03:20 PM

In practical geometry, we study geometrical constructions. The word 'construction' in geometry is used for drawing a correct and accurate figure from the given measurements. In this chapter, we shall…