Question

How do you find the Least Common Multiple of \[15,20\]?

Answer 1

Hint:To find the LCM of the numbers just use the prime factorization method. Write the numbers in a row and divide both these numbers by a common prime factor and divide until all the numbers divisible by that prime number. If the prime factor doesn’t divide a number among one of them then keep that number the same and divide the other and then finally multiply all the prime factors, we would get the LCM of numbers.

Complete step by step solution:
The given numbers are \[15,20\], to calculate the LCM of these numbers we will use the Prime Factorisation Method.
The first prime factor that divides at least one of them is \[2\] that divides \[20\] but not \[15\]. So keep \[15\] same and write the dividend of that divisible number. Similarly, follow this prime factorization.

\[2\]	\[15,20\]
\[2\]	\[15,10\]
\[3\]	\[15,5\]
\[5\]	\[5,5\]
	\[1,1\]

Since we have all the prime factors that we used in the LCM process.
Now multiply all that prime factors
\[\Rightarrow 2\times 2\times 3\times 5\]
\[\Rightarrow 60\]

Thus, we have calculated the LCM of the numbers given \[15,20\]
Hence LCM is \[60\].

Note:
The LCM is the Least Common Multiple of the numbers means the lowest number which is divisible by all those numbers whose we have to find the LCM. Another way when we have to find this is just write all the prime factors of an individual number and then for each prime factor, find where it occurs most often as a factor then write it that many times in a new row. Now multiply all those factors that we have written in a new row separately.