Least Common Multiple (LCM) of 20 and 91
The least common multiple (LCM) of 20 and 91 is 1820.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 20 and 91?
First, calculate the GCD of 20 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 91 = 0 remainder 20 |
| 2 | 91 ÷ 20 = 4 remainder 11 |
| 3 | 20 ÷ 11 = 1 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 161 | 19320 |
| 189 and 179 | 33831 |
| 14 and 31 | 434 |
| 45 and 174 | 2610 |
| 188 and 32 | 1504 |