Least Common Multiple (LCM) of 21 and 50
The least common multiple (LCM) of 21 and 50 is 1050.
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 50?
First, calculate the GCD of 21 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 50 = 0 remainder 21 |
| 2 | 50 ÷ 21 = 2 remainder 8 |
| 3 | 21 ÷ 8 = 2 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 117 | 10764 |
| 20 and 76 | 380 |
| 173 and 35 | 6055 |
| 68 and 82 | 2788 |
| 83 and 185 | 15355 |