Least Common Multiple (L.C.M.)
In the last topic we have discussed about common multiples that is same multiples of two or more numbers. Now here we will discuss about the least common multiple that is the smallest common multiple of two or more numbers.
Here are few examples illustrated on least common multiples:
1. Find the least common factor of 12 and 18
Solution:
The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84 …
The multiples of 18 are: 18, 36, 54, 72 …
The common multiples of 12 and 18 are: 36, 72 …
The least common multiple of 12 and 18 is 36
This problem can be solved by another method as well that is by complete factorization. The product of highest power of all the factors will be the least common multiple i.e. L.C.M
Alternatively,
The prime factors of 12 are: 2 × 2 × 3 = 22 × 3
The prime factors of 18 are: 2 × 3 × 3 = 32 × 2
The highest power of 2 is 22
The highest power of 3 is 32
Therefore, least common multiple of 12 and 18 is 2 × 2 × 3 × 3 = 22 × 32 = 36
2. Find the least common factor of 15 and 25
Solution:
The multiples of 15 are: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165 …
The multiples of 25 are: 25, 50, 75, 100, 125, 150, 175 …
The common multiples of 15 and 25 are: 75, 150 ….
The least common multiple of 15 and 25 is 75
3. Find the least common factor of 8 and 16
Solution:
The multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 …
The multiples of 16 are: 16, 32, 48, 64, 80, 96 …
The common multiples of 8 and 16 are: 16, 48, 64, 80, 96 ….
The least common multiple of 8 and 16 is 16
4. Find the least common factor of 20 and 30
Solution:
The multiples of 20 are: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260 …
The multiples of 30 are: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300 …
The common multiples of 20 and 30 are: 60, 120, 180, 240 …
The least common multiple of 20 and 30 is 60
5. Find the least common factor of 9 and 6
Solution:
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108 …
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72 ….
The common multiples of 9 and 6 are: 18, 36, 54, 72 …
The least common multiple of 9 and 6 is: 18
5. Find the least common factor of 21 and 14
Solution:
The multiples of 21 are: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210 ….
The multiples of 14 are: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140 …
The common multiples of 21 and 14 are: 42, 84, 126 …
The least common multiple of 21 and 14 is 42
From Least Common Multiple (L.C.M.) to HOME PAGE
Recent Articles
-
Eleventh Grade | Eleventh Grade Science | Eleventh Grade Math
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. -
Explain Digestion of Food | Salivary Glands | Oesophagus | Stomach
Jun 27, 25 12:20 AM
Before the digestion is start by the different enzymes secreted from the different digestive glands food must be turned and chut or mixed with saliva inside the mouth. -
Explain Human Digestive System | Mouth | Tongue | Pharynx | Teeth
Jun 21, 25 01:15 PM
Digestive system is a system of alimentary canal and digestive glands. Alimentary canal- alimentary canal is a tube of variable diameter having muscular wall and glandular epithelial tissues which sta… -
Vernalisation in Plants | Definition | Mechanism | Devernalization |
Jun 18, 25 01:34 PM
Definition of vernalisation- The change of flowering habit due to the low temperature treatment is known as vernalisation. This is a physiological process which was denoted by Clipart in 1857 invite b… -
The Food We Eat | Food we Get from Plants and Animals | Carbohydrates
Jun 15, 25 03:20 PM
What are the food that we should eat? Find out the names of ten food items in the word maze. Write the names in the correct column of the table given below. Food we get from plants Food we get from an…
New! Comments
Have your say about what you just read! Leave me a comment in the box below.