it wasn't an issue while i was trying to install node 12.X.X but below that it was a big pain so i followed below steps and it worked for me

Uninstalled nvm if it’s already installed using Homebrew.

brew uninstall nvm
brew cleanup

Install Rosetta

softwareupdate --install-rosetta

Make terminal/iTerm2 to open in Rosetta mode

got to Application (-> utilities) -> right click on terminal app -> get Info -> Select "Open using Rosetta" -> Restart Terminal

In Terminal run a command

arch -x86_64 zsh 

Make sure machine has .zshrc file if not just create one

cd ~
touch .zshrc

Install NVM

curl -o- https://raw.githubusercontent.com/nvm-sh/nvm/v0.39.0/install.sh | bash

And it should add the below piece of code to .zshrc

Restart the terminal and check if nvm is installed successfully by running

nvm -v

Then install Node with nvm as usual

nvm install 10

Use the following command for successful install:

curl -o- https://raw.githubusercontent.com/nvm-sh/nvm/v0.39.0/install.sh | bash

before the above command, please be sure to have .zshrc file in the root of your current username folder (~/).

Install nvm version > 0.3.7 and install node version >= 16.0

The best instructions are on nvm's own Readme's FAQ on Macs with M1 processors:

https://github.com/nvm-sh/nvm#macos-troubleshooting

I found a solution that really worked well here, am not going to write the entire steps please follow this link [Rosetta Terminal]

If you have installed nvm using homebrew and trying to install the node using command nvm install <some_version>, you will face errors on apple silicon machines (ARM) until the node version is higher than 14. Node versions older than 15 does not work on apple silicon machines (ARM) because ARM architecture is not supported by node older versions. For anything under v15, you will need to install node using Rosetta 2.

1. How to open terminal in Rosetta2 mode -> got to Application -> right click on terminal app -> get Info -> Select "Open using Rosetta" -> Restart Terminal
2. In Terminal, write -> arch -x86_64 zsh Now you will able to install any version of node (even multiple versions)