Least Common Multiple (LCM) of 21 and 41
The least common multiple (LCM) of 21 and 41 is 861.
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 41?
First, calculate the GCD of 21 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 41 = 0 remainder 21 |
| 2 | 41 ÷ 21 = 1 remainder 20 |
| 3 | 21 ÷ 20 = 1 remainder 1 |
| 4 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 112 | 1680 |
| 40 and 193 | 7720 |
| 55 and 197 | 10835 |
| 186 and 97 | 18042 |
| 78 and 77 | 6006 |