GCD and LCM
LCM = a · b / GCDGCD12
- LCM840
- The fraction a/b reduced7/10
- Coprimeno
Mathematics
Numbers
GCD and LCM, prime factors, powers, number bases, Roman numerals and combinatorics.
Prime factorization is the basis for reducing fractions and finding a common denominator: the greatest common divisor collects the shared factors, the least common multiple collects them all. This section also covers conversion between number bases, Roman numerals and combinatorics.
Calculators
8Prime factorization
n = p₁^a · p₂^b · …Factorization2³ · 3² · 5
- Number of divisors24
- Sum of divisors1,170
- Prime numberno
Powers and roots
aⁿ and ⁿ√a7 to the power of 3343
- Root of degree 31.912931
- Square root2.645751
- Square49
- Common logarithm0.845098
Division with remainder
a = b · q + rQuotient289
- Remainder3
- Exact289.428571
- Divides evenlyno
Number bases
binary · octal · hexadecimalDecimal2,026
- Binary11111101010
- Octal3752
- Hexadecimal7EA
- Number of bits11
Roman numerals
I V X L C D MRoman numeralMMXXVI
- Number of characters6
- PreviousMMXXV
- NextMMXXVII
Factorials and combinations
n! , C(n,k) = n! / (k!(n − k)!)Combinations C(n,k)120
- Permutations without repetition720
- n!3,628,800
- k!6
- 2ⁿ — every subset1,024
Rounding and scientific notation
a ≈ m · 10ⁿRounded to 2 places12,345.68
- Down12,345.67
- Up12,345.68
- Scientific notation1.2346 · 10⁴
- Whole part12,345
Tables and cheat sheets
3Powers of two
the basis of binary memory units| n | 2ⁿ | Equivalent |
|---|---|---|
| 0 | 1 | |
| 1 | 2 | |
| 2 | 4 | |
| 3 | 8 | |
| 4 | 16 | |
| 5 | 32 | |
| 6 | 64 | |
| 7 | 128 | |
| 8 | 256 | one byte — 256 values |
| 9 | 512 | |
| 10 | 1,024 | 1 KiB |
| 11 | 2,048 | |
| 12 | 4,096 | |
| 13 | 8,192 | |
| 14 | 16,384 | |
| 15 | 32,768 | |
| 16 | 65,536 | 16-bit range |
| 17 | 131,072 | |
| 18 | 262,144 | |
| 19 | 524,288 | |
| 20 | 1,048,576 | 1 MiB |
Prime numbers up to 200
there are 46 of them; two is the only even one| Range | Prime numbers | How many |
|---|---|---|
| 1–50 | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 | 15 |
| 51–100 | 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 | 10 |
| 101–150 | 101, 103, 107, 109, 113, 127, 131, 137, 139, 149 | 10 |
| 151–200 | 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 | 11 |
Roman numerals
a smaller numeral before a larger one means subtraction| Numeral | Value | Example |
|---|---|---|
| I | 1 | III = 3 |
| IV | 4 | IV = 5 − 1 |
| V | 5 | VII = 7 |
| IX | 9 | IX = 10 − 1 |
| X | 10 | XXX = 30 |
| XL | 40 | XLV = 45 |
| L | 50 | LXX = 70 |
| XC | 90 | XCIX = 99 |
| C | 100 | CCC = 300 |
| CD | 400 | CDL = 450 |
| D | 500 | DCC = 700 |
| CM | 900 | CMXC = 990 |
| M | 1000 | MMXXVI = 2026 |
Worked examples with full solutions
2Reducing a fraction by the greatest common divisor
Simplify the fraction 144/216.
- Factor the numerator
144 = 2⁴ · 3² - Factor the denominator
216 = 2³ · 3³ - The shared factors give the GCD
GCD = 2³ · 3² = 72 - Divide the numerator and the denominator
144 / 72 = 2, 216 / 72 = 3
Answer: 144/216 = 2/3 ≈ 0.6667, that is 66.67 %.
How many codes can be made
You pick 3 different digits out of 10. How many combinations are there when order does not matter, and how many when it does?
- Combinations: C(10,3)
10! / (3! · 7!) = 120 - Permutations, when order matters
120 · 3! = 720 - If the digits could repeat
10³ = 1,000 codes
Answer: 120 combinations, 720 permutations, and 1,000 codes once repeats are allowed.
Nothing matches that search.
See also
GeometryAreas and perimeters of shapes, volumes of solids, the Pythagorean theorem and trigonometry.Equations and sequencesLinear and quadratic equations, systems of two equations, arithmetic and geometric sequences.StatisticsMean, median, quartiles, standard deviation, weighted mean and points converted into grades.