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 |
|---|---|
| 50 and 41 | 2050 |
| 150 and 190 | 2850 |
| 59 and 65 | 3835 |
| 19 and 39 | 741 |
| 27 and 58 | 1566 |