im trying to authorize my org ..but i am getting this error 

when i run the below command:
 sfdx plugins:install @salesforce/lwc-dev-server
Error:
Try running: `sudo npm install -g node-gyp`
spawn node-gyp.cmd ENOENT
'nodejs' is not recognized as an internal or external command,
operable program or batch file.
Installing plugin @salesforce/lwc-dev-server... failed
    Error: yarn add @salesforce/lwc-dev-server@latest --non-interactive --mutex=file:C:\Users\hema_yejju\AppData\Local\sfdx\yarn.lock
    --preferred-cache-folder=C:\Users\hema_yejju\AppData\Local\sfdx\yarn --check-files exited with code 1
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When i run this command:npm install -g node-gyp
Error:
 Unsupported engine {
npm WARN EBADENGINE   package: 'npmlog@6.0.0',
npm WARN EBADENGINE   required: { node: '^12.13.0 || ^14.15.0 || >=16' },
npm WARN EBADENGINE   current: { node: 'v15.5.1', npm: '7.3.0' }
npm WARN EBADENGINE }
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when i run this command: sfdx plugins:install @salesforce/lwc-dev-server
Error:
Try running: `sudo npm install -g node-gyp`
spawn node-gyp.cmd ENOENT
'nodejs' is not recognized as an internal or external command,
operable program or batch file.
Installing plugin @salesforce/lwc-dev-server... failed
    Error: yarn add @salesforce/lwc-dev-server@latest --non-interactive --mutex=file:C:\Users\hema_yejju\AppData\Local\sfdx\yarn.lock
    --preferred-cache-folder=C:\Users\hema_yejju\AppData\Local\sfdx\yarn --check-files exited with code 1
PS C:\Users\hema_yejju>
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In my environment variables : i have the below 2 paths set:
C:\Program Files\Salesforce CLI\bin
C:\Program Files\nodejs\node_modules\npm\bin