Least Common Multiple (LCM) of 200 and 59
The least common multiple (LCM) of 200 and 59 is 11800.
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 200 and 59?
First, calculate the GCD of 200 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 59 = 3 remainder 23 |
| 2 | 59 ÷ 23 = 2 remainder 13 |
| 3 | 23 ÷ 13 = 1 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 12 | 2148 |
| 135 and 22 | 2970 |
| 127 and 33 | 4191 |
| 31 and 84 | 2604 |
| 109 and 162 | 17658 |