# LOWEST COMMON MULTIPLE

## About "Lowest common multiple"

Lowest common multiple :

The smallest among the common multiples of two numbers is called their least common multiple (LCM).

We can find L.C.M in two different methods

(i)   Common multiple method to find lcm

(ii)  Factorization method to find lcm

(iii) Using ladder method to find lcm

Now let us see the above methods one by one.

## Common multiple method

We have to follow the steps given below, when we use common multiple method to find the L.C.M of two or more numbers.

Step 1 :

List the multiples of the given numbers

Step 2 :

Circle and write the common multiples

Step 3 :

The smallest common multiple of is L.C.M.

Example 1 :

Find the L.C.M of 16 and 24 using common multiple method.

Solution :

Multiples of 16  =  16, 32, 48, 64, 80, 96, 112, 128, 144, 160, .........

Multiples of 24  =  24, 48, 72, 96, 120, 144, 168,.............

The smallest multiple among the common multiples is the L.C.M

Hence the L.C.M of 16 and 24 is 48.

## Factorization method

We have to follow the steps given below, when we use factorization method to find the L.C.M of two or more numbers.

Step 1 :

Find the prime factors of the given numbers.

Step 2 :

Circle the common factors.

Step 3 :

Find the product of the common factors.Multiply this product with independent factors.

Example 2 :

Find the L.C.M of 16 and 24 using factorization method.

Solution : Multiples of 16  =  2 x 2 x 2 x 2

Multiples of 24  =  2 x 2 x 3 x 2

By multiplying the common factors with independent factors, we get

=  2 x 2 x 2 x 3 x 2  =  48

Hence the L.C.M of 16 and 24 is 48.

## Using ladder method to find lcm

We use the steps given below to do prime factorization using ladder diagram.

Step 1 :

Put the given numbers inside the "L" shape

Step 2 :

We have to split the given number by prime numbers only. That is,  always we have to put prime numbers out side the "L" shape.

Given below will be helpful to find the prime number which exactly divides the given number.

• A number which ends with 0, 2, 4, 6 and 8 is divisible by the smallest prime number 2.
• A number which ends with 0 or 5 is divisible by 5
• If the sum of digits of the given number is a multiple of 3, then the given number is divisible by 3.

Step 4 :

Repeat this process until get prime numbers inside the ladder.

Step 5 :

The product of numbers inside and out side the ladder will be the L.C.M

Example 3 :

Find the L.C.M of 16 and 24 using ladder diagram

Solution : L.C.M of 16 and 24  =  2 x 2 x 2 x 2 x 3

=  48 After having gone through the stuff given above, we hope that the students would have understood "Lowest common multiple".

Apart from the stuff given above, if you want to know more about "Lowest common multiple", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments... WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6