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.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
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
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
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
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 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
