To find Least Common Multiple by using Prime Factorization Method

To find least common multiple by using prime factorization method is discussed here. 

To find the LCM of two or more numbers, we first find all the prime factors of the given numbers and write them one below the other. Take one factor from each common group of factors and find their product. Multiply the product with other ungrouped factors. The resultant is the LCM of given numbers.


Step I: 

Resolve each given number into its prime factors and express the factors obtained in exponent form. 

Step I: 

Find the product of the highest powers of all the factors that occur in any of the given numbers. 


Step III: 

The product obtained in Step II is the required least common multiple (L.C.M). 


For example:

1. Find the least common multiple (L.C.M) of 9 and 15 by using prime factorization method.

Solution:

Step I:

Resolving each given number into its prime factors.

9 = 3 × 3 = 3².

15 = 3 × 5.



Step II:

The product of all the factors with highest powers.

= 3^2 × 5 = 3 × 3 × 5 = 45.



Step III:

The required least common multiple (L.C.M) of 9 and 15 = 45.



2. What is the least common multiple (L.C.M) of 16 and 28 by using prime factorization method?

Solution:

Step I:

Resolving each given number into its prime factors.

16 = 2 × 2 × 2 × 2 = 24.

28 = 2 × 2 × 7 = 22 × 7.



Step II:

The product of all the factors with highest powers.

= 24 × 7 = 2 × 2 × 2 × 2 ×7 = 112.



Step III:

The required least common multiple (L.C.M) of 16 and 28 = 112.


3. Find the LCM of 32, 48 and 72 by prime factorization.

Solution:


LCM of 32, 48 and 72

LCM of 32, 48 and 72 = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288

● 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 To find Least Common Multiple by using Prime Factorization Method to HOME PAGE


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.



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.



Share this page: What’s this?

Recent Articles

  1. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Mar 02, 24 05:31 PM

    Fractions
    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Subtraction of Fractions having the Same Denominator | Like Fractions

    Mar 02, 24 04:36 PM

    Subtraction of Fractions having the Same Denominator
    To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numera…

    Read More

  3. Addition of Like Fractions | Examples | Worksheet | Answer | Fractions

    Mar 02, 24 03:32 PM

    Adding Like Fractions
    To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

    Read More

  4. Comparison of Unlike Fractions | Compare Unlike Fractions | Examples

    Mar 01, 24 01:42 PM

    Comparison of Unlike Fractions
    In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a nu…

    Read More

  5. Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

    Feb 29, 24 05:12 PM

    Equivalent Fractions
    The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

    Read More