Least Common Multiple (LCM) of 59 and 41
The least common multiple (LCM) of 59 and 41 is 2419.
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 59 and 41?
First, calculate the GCD of 59 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 41 = 1 remainder 18 |
| 2 | 41 ÷ 18 = 2 remainder 5 |
| 3 | 18 ÷ 5 = 3 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 24 | 2280 |
| 65 and 89 | 5785 |
| 71 and 47 | 3337 |
| 18 and 85 | 1530 |
| 160 and 84 | 3360 |