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
-
Definition of Respiratory Quotient | calculation | Application | Plant
Dec 02, 24 12:09 AM
Definition of respiration quotient- the ratio of the carbon-dioxide evolved to that of the oxygen consumed by a cell, tissue, plants or animals in a given time is called respiratory quotient. It is us… -
Amphibolic Pathway | Definition | Examples | Pentose Phosphate Pathway
Jun 06, 24 10:40 AM
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… -
Respiratory Balance Sheet | TCA Cycle | ATP Consumption Process
Feb 18, 24 01:56 PM
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… -
Electron Transport System and Oxidative Phosphorylation | ETC |Diagram
Feb 04, 24 01:57 PM
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… -
Tricarboxylic Acid Cycle | Krebs Cycle | Steps | End Products |Diagram
Jan 28, 24 12:39 PM
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…
New! Comments
Have your say about what you just read! Leave me a comment in the box below.