Question
Find the $LCM$ of $12$ and $18.$
✓
Answer
Clearly, we can see that common multiples of $12$ and $18$ are: $36, 72, 108$ etc
The lowest of these is $36.$
Now, Let us see another method to find $LCM$ of these two numbers.
The prime factorization of $12$ and $18$ are :
$12 = 2 \times 2 \times 3;$
$18 = 2 \times 3 \times 3$
In these prime factorizations, the maximum number of times the prime factor $2$ occurs is two; this happens for $12.$ Similarly, the maximum number of times the factor $3$ occurs is two; this happens for $18.$ The $LCM$ of the two numbers is the product of the prime factors counted the maximum number of times they occur in any of the numbers.
Thus, in this case: $LCM = 2 \times 2 \times 3 \times 3 = 36.$
The lowest of these is $36.$
Now, Let us see another method to find $LCM$ of these two numbers.
The prime factorization of $12$ and $18$ are :
$12 = 2 \times 2 \times 3;$
$18 = 2 \times 3 \times 3$
In these prime factorizations, the maximum number of times the prime factor $2$ occurs is two; this happens for $12.$ Similarly, the maximum number of times the factor $3$ occurs is two; this happens for $18.$ The $LCM$ of the two numbers is the product of the prime factors counted the maximum number of times they occur in any of the numbers.
Thus, in this case: $LCM = 2 \times 2 \times 3 \times 3 = 36.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The following table gives information about the circulation of newspapers (dailies) in a town in five languages.
Prepare a pictograph of the above data, using a symbol of your choice, each representing $1000$ newspapers.
→| Language: | English | Hindi | Tamil | Punjabi | Gujarati |
| Number of newspapers: | $5000$ | $8500$ | $500$ | $2500$ | $1000$ |
Read the following bar graph and answer the following questions:
$i.\ $What information is given by the bar graph?
$ii.\ $In which year the export is minimum?
$iii.\ $In which year the import is maximum?
$iv.\ $In which year the difference of the value of export and import is maximum?
→$i.\ $What information is given by the bar graph?
$ii.\ $In which year the export is minimum?
$iii.\ $In which year the import is maximum?
$iv.\ $In which year the difference of the value of export and import is maximum?
Draw any circle on the graph paper. Count the squares and use them to estimate the area of the circular region.
Use a pair of compasses and construct the following angles: $15^\circ $
→Construct with ruler and compasses, angles of measure: $30^\circ $
→How many right angles do you make if you start facing south and turn to north?
If a bus travels $126\ km$ in $3$ hours and a train travels $315\ km$ in $5$ hours, then the ratio of their speeds is:
→Construct a rectangle whose adjacent sides are $8\ cm$ and $3\ cm.$
→Draw an angle of $60^\circ ,$ using a pair of compasses. Bisect it to make an angle of $30^\circ .$
→Give three examples of line segments from your environment.