Time and work problems are a permanent fixture in CSAT, MPSC, and banking exams. Most students waste precious minutes using traditional fractional methods (like assuming total work is 1). Today, we will master the LCM Method, which eliminates fractions entirely and lets you solve these problems mentally in under 30 seconds.
The Traditional Method vs. The LCM Shortcut
When a traditional textbook says “A does a job in 10 days, so A’s 1-day work is 1/10,” it introduces fractions. Dealing with fractions leads to calculation errors under exam pressure.
The LCM Method assumes the total work is the Least Common Multiple (LCM) of the given days. This converts the entire problem into simple whole numbers representing “Units of Work per Day” (Efficiency).
Step-by-Step Practical Examples
Example 1: Basic Two-Person Problem Question: A can complete a piece of work in 12 days, and B can complete the same work in 15 days. If they work together, how many days will they take to finish the work?
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Step 1: Find the Total Work (LCM). Find the LCM of 12 and 15. The LCM is 60. Let’s assume the total work is 60 units.
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Step 2: Calculate Individual Efficiency (Work per day).
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A’s efficiency = 60 ÷ 12 = 5 units/day
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B’s efficiency = 60 ÷ 15 = 4 units/day
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Step 3: Combine Their Efficiencies. Combined efficiency of (A + B) = 5 + 4 = 9 units/day.
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Step 4: Find the Total Time Taken.
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Time = (Total Work) ÷ (Total Efficiency)
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Time = 60 ÷ 9 = 6.66 days (or 6 and 2/3 days)
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