Question

lcm of 102,136,150,170​

Answer 1

Hello , how are you doing ?

Well my friend , the statement of the question ask for we find the least common multiple of 102, 136, 150 and 170. Now, we make the following question : How we will solve it?

- The explanation is very simple, we can solve it using the method prime factorization. See the resolution below in the practice.

$\begin{array}{r|l}102,136,150,170&2\\51,68,75,85&2\\51,34,75,85&2\\51,17,75,85&3\\17,17,25,85&5\\17,17,5,17&5\\17,17,1,17&17\\1,1,1,1\end{array}$

Now, that you factored 102, 136, 150 and 170 you can find the least common multiple.

$\mathsf{\textbf{LCM}=2\cdot2\cdot2\cdot3\cdot5\cdot5\cdot17} \\\\ \mathsf{\textbf{LCM}=2^{3}\cdot3\cdot5^{2}\cdot17} \\\\ \mathsf{\textbf{LCM}=8\cdot3\cdot25\cdot17} \\\\ \mathsf{\textbf{LCM}=24\cdot25\cdot17} \\\\ \mathsf{\textbf{LCM}=600\cdot17} \\\\ \boxed{\mathsf{\textbf{LCM=10200}}}$

Therefore, with all this conjecture that make with objective of find the least common multiple of 102, 136, 150 and 170 we have the conclusion that the least common multiple is 10200.

I have I have collaborated !