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.
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
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
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.
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.
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
Worksheet on Divisibility Rules | Questions on Test of Divisibility
This is a worksheet which will provide few problems on the divisibility rule of 2, 3, 4, 5, 6, 7, 8, 9, and 10. 1. Check whether the following numbers are divisible by 2 or 3 or both? (i) 2562 (ii) 5693 (iii) 2201 (iv) 7480 (v) 5296 (vi) 4062 (vii) 4568 (viii) 1425 (ix) 1110
Problems on Divisibility Rules | Rules to Test of Divisibility | Test
Here are few problems on the divisibility rules of 2, 3, 4, 5, 6, 7, 8, 9, and 10 which will help the learners in revising their concepts on the divisibility rules. 1. Check whether 3456 is divisible by 2? Solution: The last digit is an even number (i.e. 6) hence 3456 is
From To Find Least Common Multiple by using Prime Factorization Method to HOME PAGE
Recent Articles
-
Mechanism of Breathing | Definition of Inspiration and Expiration
Aug 17, 25 11:41 PM
Breathing is the process which is accomplished in three states that is inspiration expiration and pause . Definition of inspiration - Entry of air into the lungs from outside during breathing is calle… -
Human Respiratory System | External Nares | Nasal Cavity | Pharynx
Aug 04, 25 03:14 PM
Definition of respiration - This is the process of making energy available to organisms and their living cells through enzyme controlled catabolic breakdown of organic molecules. The organic materials… -
Disorders of Digestive System | Symptoms of Jaundice | Vomiting |
Jul 16, 25 12:18 PM
Jaundice- It is a disease that occurs due to Umesh discoloration of the skin due to deposition of bilirubin and biliverdin pigment. Jaundice can be offered according to the different position like pre… -
Absorption of Digested Products | Absorption of Water | Nephrons
Jul 09, 25 02:24 PM
Food and water is observed in different parts of the body and is distributed in different cells and tissues. Absorption of food is observed to be observed in the small intestine in the specific type o… -
Eleventh Grade | Eleventh Grade Science | Eleventh Grade Biology
Jun 27, 25 12:26 AM
Eleventh grade biology has been designed in accordance with the recommended topics. We will cover all the topics in biology very exciting and interesting way.
New! Comments
Have your say about what you just read! Leave me a comment in the box below.