One advantage of focusing on stocks within the Dow Jones Industrials (DJINDICES:^DJI) is that you largely don't have to worry about weeding out bad companies. Especially in light of its recent realignment, the Dow has a strong track record of identifying the leaders of various industries with good potential for sustained future growth. That makes it easier to look for Dow stocks with attractive valuations without worrying too much about threats to their underlying business models.

With that goal in mind, let's look at the three cheapest Dow stocks by earnings multiple. Although using price-to-earnings ratios is simplistic and can be misleading, it's a reasonable first place to start in combing through the 30 components of the Dow.

JPMorgan Chase (NYSE:JPM), 8.8 P/E
Banking giant JPMorgan weighs in with the lowest earnings multiple in the Dow, based on data from Yahoo! Finance. However, that status won't last for very long. JPMorgan's earnings report yesterday morning led to a massive litigation-related loss for the third quarter that will sink the bank's trailing earnings over the past 12 months. In turn, JPMorgan can expect its P/E to climb somewhat.

In many ways, though, this reveals the flaws of the P/E ratio more than it does problems at JPMorgan. Admittedly, a $7.2 billion after-tax charge is a hard thing to ignore. But if you consider those losses to be one-time in nature -- a heroic assumption given the $23 billion that JPMorgan has set aside in total to cover legal settlements, regulatory fines, and other costs -- then the bank remains solidly profitable. JPMorgan even managed to boost its earnings from last year's third quarter on an adjusted basis. Even with impressive share-price gains in recent years, JPMorgan still looks like a relative bargain.

Chevron (NYSE:CVX), 9.5 P/E
Oil major Chevron also has an earnings multiple below 10, making its stock look like a good value. But the oil company has faced some troubles recently, as maintaining production levels becomes more difficult. Just earlier this week, Chevron released interim results for the third quarter and warned that its earnings would be likely to decline sequentially. In particular, U.S. production volumes were lower during July and August than in the second quarter.

Still, Chevron is a global player in energy, and new opportunities overseas have so far managed to offset sluggish domestic production. With an emphasis on developing natural-gas assets around the world, Chevron hopes to build a worldwide network of gas production and transportation through strategically placed liquefied natural gas terminals and other transmission infrastructure. Despite challenges, Chevron looks prepared to face tough conditions head on and still find growth.

Goldman Sachs (NYSE:GS), 9.8 P/E
As with JPMorgan, Goldman Sachs is dealing with a tough environment for financial companies. Rising interest rates have raised the specter of declining earnings for investment bankers. After enjoying huge profits from underwriting massive amounts of bond offerings, Goldman and its peers now have to find ways to replace that disappearing income now that the refinancing cycle has largely ended.

Goldman offers a wide array of financial services, many of which aren't as sensitive to rates as its bond underwriting business. With a booming IPO market and plenty of merger and acquisition activity, Goldman is still among the top choices for financial advisory services to corporations seeking to make strategic moves in the capital markets. Even if Goldman has a temporary setback, its share price gives it a margin of safety that should be adequate for anything short of a full-blown relapse of the financial crisis.

It's important to understand that attractive valuations won't necessarily prevent share-price declines at any of these three stocks. But with solid businesses behind them, they offer good long-term prospects that make now seem like a good time for interested investors to buy.

Fool contributor Dan Caplinger owns warrants on JPMorgan Chase. You can follow him on Twitter: @DanCaplinger. The Motley Fool recommends Chevron and Goldman Sachs and owns shares of JPMorgan Chase. Try any of our Foolish newsletter services free for 30 days. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.