Least Common Multiple (LCM) of 21 and 183
The least common multiple (LCM) of 21 and 183 is 1281.
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 21 and 183?
First, calculate the GCD of 21 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 183 = 0 remainder 21 |
| 2 | 183 ÷ 21 = 8 remainder 15 |
| 3 | 21 ÷ 15 = 1 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 100 | 2700 |
| 83 and 117 | 9711 |
| 142 and 123 | 17466 |
| 19 and 180 | 3420 |
| 40 and 187 | 7480 |