Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

Find the common multiples of 3, 4 and 9.

Answer
VerifiedVerified
478.8k+ views
like imagedislike image
Hint:
Here, we will find the common multiples of the numbers by using the least common multiples of the given number. A common multiple of a number is defined as a whole number that is a shared multiple of each set of the numbers.

Complete step by step solution:
We are given with the numbers 3, 4 and 9.
We will first find the Least common multiple of the given number.
3|3493|1432|1412|1211|111
So, the least common multiple of the given number is given by
LCM(3,4,9)=3×3×2×2
Multiplying the terms, we get
LCM(3,4,9)=36
So, the least common multiple of the numbers 3, 4, 9 is 36.
Now, we will find the common multiples of the numbers 3, 4, 9
The common multiples of the numbers are the multiples of the least common multiple of the number.
So, the common multiples of the numbers is given by
36×1=36
36×2=72
36×3=108

Therefore, the common multiples of the numbers of 3,4,9 is 36,72,108,............

Note:
We know that a number can have an infinite number of multiples. Therefore, any two or more set two numbers can have an infinite number of common multiples. The smallest common multiple is the L.C.M of the given numbers.
We can also find the common multiples of the given numbers from the multiples of the numbers.
3×1=33×2=63×3=93×4=123×5=153×6=183×7=213×8=243×9=273×10=303×11=333×12=363×13=393×14=423×15=45| 4×1=44×2=84×3=124×4=164×5=204×6=244×7=284×8=324×9=364×10=404×11=444×12=484×13=524×14=564×15=60| 9×1=99×2=189×3=279×4=369×5=459×6=549×7=639×8=729×9=819×10=909×11=999×12=1089×13=1179×14=1269×15=135
Here, from the multiplication table, we can see that only 36 is common to all 3 numbers till the 15th multiple.
Therefore, we can say that the common multiples of the numbers 3, 4, 9 is 36.
WhatsApp Banner