Adding fractions: 1/4 + 1/6 + 1/8
LCM(4, 6, 8): prime factors 4=2², 6=2×3, 8=2³. Take 2³ × 3 = 24. So 1/4 = 6/24, 1/6 = 4/24, 1/8 = 3/24. Sum: 13/24. Without LCM, fraction addition would be guesswork.
LCM Calculator - حاسبة مجانية على الإنترنت
Find the Least Common Multiple - the smallest positive integer divisible by every number in your list. Essential for adding fractions with different denominators and for scheduling problems.
- الصيغة معروضة في الصفحة
- تعمل في متصفحك
- مدخلاتك تبقى خاصة
Enter two or more positive integers, separated by commas, spaces or new lines
LCM (Least Common Multiple)
72
GCF / HCF / GCD
6
Prime factorisation
- 12 = 2 × 2 × 3
- 18 = 2 × 3 × 3
- 24 = 2 × 2 × 2 × 3
لا يزال بعض المحتوى معروضًا بالإنجليزية.
فهم LCM Calculator
LCM (Least Common Multiple) is the smallest positive integer that two or more numbers all divide into evenly. It's introduced in Class 5-6 mathematics and remains essential through to Class 10 and beyond. The most common school use is adding or subtracting fractions with different denominators - to add 1/4 + 1/6, you need a common denominator, which is LCM(4, 6) = 12. Beyond fractions, LCM solves real-world synchronisation problems: when do two periodic events coincide? Two buses departing at different intervals, two gears with different teeth, two signal lights flashing at different rates - all use LCM math.
This calculator handles two or more positive integers and returns the LCM along with the prime factorisation that produced it. The factorisation display helps Class 6-8 students learn the prime-power method (take the highest power of each prime appearing in any number, multiply them together). It also handles fractional inputs via the formula LCM of fractions = LCM(numerators) / GCD(denominators) - useful when adding fractions like 1/3 + 1/5 + 2/15. Works fully offline once loaded.
استخدام LCM Calculator في 2 خطوات
Enter two or more positive integers, separated by commas.
Read the LCM and the prime factorisation used to compute it.
كيف تعمل LCM Calculator
For two numbers, LCM(a,b) = (a × b) / GCD(a,b). For more, fold pairwise: LCM(a,b,c) = LCM(LCM(a,b), c). The prime-factorisation method takes the highest power of each prime appearing in any number.
Formula
LCM(a, b) = |a × b| / GCD(a, b)
- a, bPositive integers
- GCDGreatest common divisor
كيف تصل LCM Calculator إلى النتيجة
Two methods to compute LCM. Method 1 - using GCD: LCM(a, b) = (a × b) / GCD(a, b). For example, LCM(12, 18) = (12 × 18) / GCD(12, 18) = 216 / 6 = 36. Method 2 - prime factorisation: factor each number into primes, then take the highest power of each prime that appears anywhere. 12 = 2² × 3; 18 = 2 × 3². Highest power of 2: 2². Highest power of 3: 3². LCM = 4 × 9 = 36.
For more than two numbers, both methods generalise. With GCD method: LCM(a, b, c) = LCM(LCM(a, b), c) - fold pairwise. With prime factorisation: take the highest power of every prime appearing in any of the numbers. Prime factorisation is often faster for many small numbers; GCD method is faster for two large numbers.
The relationship LCM × GCD = product (for two numbers) is a fundamental result. It means that once you know either LCM or GCD, you can compute the other instantly using a × b = LCM × GCD. This is also why LCM grows large when the numbers share few common factors - coprime numbers have GCD = 1, so their LCM is their product.
أمثلة محلولة
Two buses departure synchronisation
Bus A leaves every 15 min, Bus B every 25 min. Both leave together at 9 AM. When do they next leave together? LCM(15, 25) = 75 min. Next coincidence: 9:00 + 1h 15min = 10:15 AM.
Setting traffic light cycle for synchronised wave
Three lights with cycles 60s, 90s, 120s. To synchronise all three: LCM(60, 90, 120) = 360 seconds = 6 minutes. They all reset together every 6 minutes.
متى تستخدم LCM Calculator
- Class 5-10 mathematics - fraction addition/subtraction homework.
- Scheduling - finding when periodic events synchronise.
- Engineering - gear ratios, signal cycles, traffic light timing.
- Music - finding pulse alignment in polyrhythmic compositions.
- Computer science - modular arithmetic and cycle length problems.
- Number theory - building blocks of divisibility analysis.
- Project planning - task cycle alignment.
- Astronomy - orbital period alignments (planets, satellites).
أخطاء ومزالق شائعة
- Computing LCM by multiplying all numbers. LCM(12, 18) = 36, not 216.
- Confusing LCM with GCD. LCM is the smallest common multiple; GCD is the largest common divisor.
- Forgetting that LCM is always ≥ the largest input number.
- Using LCM on non-positive integers without care. LCM is defined for positive integers; treat 0 and negatives specially.
- Trying to take LCM of non-integer values directly. Convert to a common fractional form first.
استفد أكثر من هذه الأداة
- For two numbers, GCD method is fastest: LCM = (a × b) / GCD(a, b).
- For three or more numbers, prime factorisation is often clearer.
- Always check: LCM should be a multiple of every input number.
- Use LCM whenever you see different cycle lengths and need to find their alignment.
- Pair with the GCF/GCD, factor and fraction calculators on this site for related number theory work.
أسئلة حول LCM Calculator
Why is LCM useful?
Adding fractions: ½ + ⅓ needs the LCM of 2 and 3 (which is 6). Then ½ = 3/6, ⅓ = 2/6, so the sum is 5/6.
Real-world LCM examples?
Two buses leave at different intervals - when do they leave together again? That's an LCM problem. Same for gear teeth meshing or signal cycles aligning.
How is LCM related to GCD?
Tightly - LCM × GCD = product of the two numbers. So once you know GCD, LCM follows immediately.
What's LCM(12, 18)?
36. Because GCD(12, 18) = 6, and 12 × 18 / 6 = 216 / 6 = 36.
Can I compute LCM of fractions?
Yes - LCM of fractions = LCM(numerators) / GCD(denominators). Useful when adding fractions with non-integer denominators.
What if one number is 0?
LCM(0, anything) is conventionally 0. Most calculators (including this one) treat zero gracefully but the result is rarely useful.
Math in your browser
From simple percentages to scientific notation, statistics, geometry and big-number arithmetic - every common math problem you'd reach for a calculator for, runs in your browser with no installs. The fraction calculator preserves exact rationals, the big-number calculator uses BigInt for hundreds of digits without precision loss, and the scientific calculator's expression evaluator is a hand-written shunting-yard parser (no eval) that supports trig, log, factorial and parentheses.
If you're a student, double-check your work without paying for a graphing calculator. If you're a professional, use these tools as a sanity check on spreadsheet formulas. Every result is shown alongside its formula and inputs, so the math is always auditable.
The LCM Calculator is part of the Math suite on Online Calculator Tools, alongside 6 related calculators. All tools share the same UI patterns, the same privacy-first rendering (nothing is sent to a server), and the same commitment to showing the formula and assumptions behind every result.