how magento getting configurable product lowest price of associated products?

You have to make plugin for that to display max price inside detail page, Below is step by step module for your need,

Filepath, app/code/Vendor/Modulename/

Registration file, app/code/Vendor/Modulename/registration.php

<?php
\Magento\Framework\Component\ComponentRegistrar::register(
    \Magento\Framework\Component\ComponentRegistrar::MODULE,
    'Vendor_Modulename',
    __DIR__
);

app/code/Vendor/Modulename/etc/module.xml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Module/etc/module.xsd">
    <module name="Vendor_Modulename" setup_version="2.0.0">
    </module>
</config>

app/code/Vendor/Modulename/etc/frontend/di.xml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
    <type name="Magento\ConfigurableProduct\Pricing\Price\ConfigurablePriceResolver">
            <plugin name="pricemaxindetail" type="Vendor\Modulename\Pricing\ConfigurablePrice"/>
    </type>
</config>

app/code/Vendor/Modulename/Pricing/ConfigurablePrice.php

Inside this file, you have to pluginize resolveprice() function

<?php
/**
 * Copyright © 2016 Magento. All rights reserved.
 * See COPYING.txt for license details.
 */

namespace Vendor\Modulename\Pricing;

class ConfigurablePrice
{
    protected $_moduleManager;
    protected $_jsonEncoder;
    protected $_registry;


    public function __construct(
        \Magento\Framework\Module\Manager $moduleManager,
        \Magento\Framework\Json\EncoderInterface $jsonEncoder,
        \Magento\Framework\Registry $registry,           
        \Magento\Catalog\Api\ProductRepositoryInterface $productRepository,         
        \Magento\Catalog\Api\Data\ProductInterfaceFactory $productFactory,    
        \Magento\ConfigurableProduct\Model\Product\Type\Configurable $configurableType,
        \Magento\Framework\Api\DataObjectHelper $dataObjectHelper,
        \Magento\CatalogInventory\Api\StockStateInterface $stockState,
        array $data = [] 
    )
    {
        $this->_moduleManager = $moduleManager;
        $this->_jsonEncoder = $jsonEncoder;
        $this->_registry = $registry;
        $this->productFactory = $productFactory;      
        $this->productRepository = $productRepository;       
        $this->_configurableType = $configurableType;        
        $this->dataObjectHelper = $dataObjectHelper;   
        $this->stockState = $stockState; 
    }

    /**
     * @param \Magento\Framework\Pricing\SaleableInterface|\Magento\Catalog\Model\Product $product
     * @return float
     * @throws \Magento\Framework\Exception\LocalizedException
     */
    public function aroundResolvePrice($subject, \Closure $proceed,\Magento\Framework\Pricing\SaleableInterface $product)
    {
        $price = null; 
        //get parent product id      
        $parentId = $product['entity_id'];
        $childObj = $this->getChildProductObj($parentId);
        foreach($childObj as $childs){
            $productPrice = $childs->getPrice();
            $price = $price ? max($price, $productPrice) : $productPrice;
        }
        return $price;        
        //return (float)$proceed($product['entity_id']);
    }

     public function getProductInfo($id){    
        //get product obj using api repository...          
        if(is_numeric($id)){           
            return $this->productRepository->getById($id); 
        }else{
            return;
        } 
    }

    public function getChildProductObj($id){
        $product = $this->getProductInfo($id);
        //if quote with not proper id then return null and exit;
        if(!isset($product)){
            return;
        }

        if ($product->getTypeId() != \Magento\ConfigurableProduct\Model\Product\Type\Configurable::TYPE_CODE) {
            return [];
        }

        $storeId = 1;//$this->_storeManager->getStore()->getId();
        $productTypeInstance = $product->getTypeInstance();
        $productTypeInstance->setStoreFilter($storeId, $product);
        $childrenList = [];       

        foreach ($productTypeInstance->getUsedProducts($product) as $child) {
            $attributes = [];
            $isSaleable = $child->isSaleable();

            //get only in stock product info
            if($isSaleable){
                foreach ($child->getAttributes() as $attribute) {
                    $attrCode = $attribute->getAttributeCode();
                    $value = $child->getDataUsingMethod($attrCode) ?: $child->getData($attrCode);
                    if (null !== $value && $attrCode != 'entity_id') {
                        $attributes[$attrCode] = $value;
                    }
                }

                $attributes['store_id'] = $child->getStoreId();
                $attributes['id'] = $child->getId();
                /** @var \Magento\Catalog\Api\Data\ProductInterface $productDataObject */
                $productDataObject = $this->productFactory->create();
                $this->dataObjectHelper->populateWithArray(
                    $productDataObject,
                    $attributes,
                    '\Magento\Catalog\Api\Data\ProductInterface'
                );
                $childrenList[] = $productDataObject;
            }
        }

        $childConfigData = array();
        foreach($childrenList as $child){
            $childConfigData[] = $child;
        }

        return $childConfigData;
    }

}

run command

php bin/magento setup:upgrade

remove var folder and check in frontend

See \Magento\ConfigurableProduct\Pricing\Price\ConfigurablePriceResolver::resolvePrice. It's method resposible for calculation the price of configurable product based on child price.

You can pluginize it and implements your algorithm.