To Find Least Common Multiple by using Prime Factorization Method

This topic would discuss about how to find the least common multiple by using prime factorization method.

Steps to find out the least common multiple by using prime factorization method:

Step I: First find all the prime factors of the given number

Step II: Then write all the prime factors in exponential form

Step III: Then find the product of highest power of all the prime factors.

Here are few examples to illustrate least common multiple by using prime factorization method:

1. Find the least common factor of 256 and 224 by using prime factorization method.

To Find Least Common Multiple by using Prime Factorization Method

The factors of 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 28

The factors of 224 = 2 × 2 × 2 × 2 × 2 × 7 = 25 × 7

The highest power of 2 is 28

The highest power of 7 is 7

The least common multiple of 256 and 224 = 28 × 5 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 = 1792


2. Find the least common factor of 105 and 110 by using prime factorization method

To Find Least Common Multiple by using Prime Factorization Method

The factors of 105 = 5 × 3 × 7 

The factors of 110 = 2 × 5 × 11

The highest power of 2 is 2

The highest power of 3 is 3

The highest power of 5 is 5

The highest power of 7 is 7

The highest power of 11 is 11

The least common multiple of 105 and 110 = 2 × 3 × 5 × 7 ×11 = 2310

Note:

Here we can see that there are no common factors hence all the factors of both the number are required to be multiplied to find the L.C.M


3. Find the least common factor of 48 and 60 by using prime factorization method

To Find Least Common Multiple by using Prime Factorization Method

The factors of 48 = 2 × 2 × 2 × 2 × 3 = 24 × 3

The factors of 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5

The highest power of 2 is 24

The highest power of 3 is 3

The highest power of 5 is 5

The least common multiple of 48 and 60 = 24 × 5 × 3 = 2 × 2 × 2 × 2 × 3 × 5 = 240


4. Find the least common factor of 21 and 42 by using prime factorization method.

To Find Least Common Multiple by using Prime Factorization Method

The factors of 21 = 3 × 7

The factors of 42 = 2 × 3 × 7 

The highest power of 2 is 2

The highest power of 3 is 3

The highest power of 7 is 7

The least common multiple of 21 and 42 = 2 × 3 × 7 = 42


5. Find the least common factor of 44 and 88 by using prime factorization method.

To Find Least Common Multiple by using Prime Factorization Method

The factors of 44 are: 2 × 2 × 11 = 22 × 11

The factors of 88 are: 2 × 2 × 2 × 11 = 23 × 11

The highest power of 2 is 23 × 11

The highest power of 11 is 11

The least common multiple of 44 and 88 is 2 × 2 × 2 × 11 = 23 × 11 = 88.

You might like these



5th Grade Math

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.


Recent Articles

  1. Amphibolic Pathway | Definition | Examples | Pentose Phosphate Pathway

    Jun 06, 24 10:40 AM

    Amphibolic Pathway
    Definition of amphibolic pathway- Amphibolic pathway is a biochemical pathway where anabolism and catabolism are both combined together. Examples of amphibolic pathway- there are different biochemical…

    Read More

  2. Respiratory Balance Sheet | TCA Cycle | ATP Consumption Process

    Feb 18, 24 01:56 PM

    ATP Synthase in Mitochondria
    The major component that produced during the photosynthesis is Glucose which is further metabolised by the different metabolic pathways like glycolysis, Krebs cycle, TCA cycle and produces energy whic…

    Read More

  3. Electron Transport System and Oxidative Phosphorylation | ETC |Diagram

    Feb 04, 24 01:57 PM

    Electron Transport Chains
    It is also called ETC. Electron transfer means the process where one electron relocates from one atom to the other atom. Definition of electron transport chain - The biological process where a chains…

    Read More

  4. Tricarboxylic Acid Cycle | Krebs Cycle | Steps | End Products |Diagram

    Jan 28, 24 12:39 PM

    Aerobic Respiration
    This is a type of process which execute in a cyclical form and final common pathway for oxidation of Carbohydrates fat protein through which acetyl coenzyme a or acetyl CoA is completely oxidised to c…

    Read More

  5. Aerobic Respiration | Definition of Aerobic Respiration | Glycolysis

    Dec 15, 23 08:42 AM

    Aerobic Respiration
    This is a type of respiration where molecular free oxygen is used as the final acceptor and it is observed in cell. Site of Aerobic Respiration - Aerobic respiration is observed in most of the eukaryo…

    Read More