Examples to find Least Common Multiple by using Prime Factorization Method

Examples to find least common multiple by using prime factorization method are discussed here.

We write the prime factorization of each of the given numbers. Then, the required LCM of these numbers is the product of all different prime factors of the numbers using the greatest power of each common prime factor.


1. What is the least common multiple (L.C.M) of 21 and 49 by using prime factorization method?

Solution:


To find the LCM, multiply all prime factors. But the common factors are included only once.

21 = 3 × 7. 

49 = 7 × 7 = 7². 

= 3 × 7² = 3 × 7 × 7 = 147. 

The required least common multiple (L.C.M) of 21 and 49 = 98. 



2. What is the least common multiple (L.C.M) of 36 and 14 by using prime factorization method?

Solution:



To find the LCM, multiply all prime factors. But the common factors are included only once.

36 = 2 × 2 × 3 × 3 = 2² × 3².

14 = 2 × 7.

= 2² × 3² × 7 = 2 × 2 × 3 × 3 × 7 = 252.

The required least common multiple (L.C.M) of 36 and 14 = 252.



3. What is the least common multiple (L.C.M) of 5, 4 and 16 by using prime factorization method?

Solution:



To find the LCM, multiply all prime factors. But the common factors are included only once.

5 = 5 × 1.

4 = 2 × 2.

16 = 2 × 2 × 2 × 2 = 2⁴.

= 2⁴ × 5 = 2 × 2 × 2 × 2 × 5 = 80.

The required least common multiple (L.C.M) of 5, 4 and 16 = 80.



4. Find L.C.M of 504 and 594 by prime factorization method.

Solution:



To find the LCM, multiply all prime factors. But the common factors are included only once.

504 = 2 × 2 × 2 × 3 × 3 × 7 = 2³ × 3³ × 7.

594 = 2 × 3 × 3 × 3 × 11 = 2 × 3³ × 11.

= 2³ × 3³ × 7 × 11 = 2 × 2 × 2 × 3 × 3 × 3 × 7 × 11 = 16632.

The required least common multiple (L.C.M) of 504 and 594 = 16632.



These are the four examples to find least common multiple by using prime factorization method.


● Multiples.

Common Multiples.

Least Common Multiple (L.C.M).

To find Least Common Multiple by using Prime Factorization Method.

Examples to find Least Common Multiple by using Prime Factorization Method.

To Find Lowest Common Multiple by using Division Method

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

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

Relationship between H.C.F. and L.C.M.

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.





5th Grade Numbers Page 

5th Grade Math Problems 

From Examples to find Least Common Multiple by using Prime Factorization Method to HOME PAGE




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.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Converting Fractions to Decimals | Solved Examples | Free Worksheet

    Apr 28, 25 01:43 AM

    Converting Fractions to Decimals
    In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

    Read More

  2. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Apr 27, 25 10:13 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  3. Converting Decimals to Fractions | Solved Examples | Free Worksheet

    Apr 26, 25 04:56 PM

    Converting Decimals to Fractions
    In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…

    Read More

  4. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Apr 26, 25 03:48 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  5. Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table

    Apr 26, 25 01:00 PM

    Multiplication Table of Four
    Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times

    Read More