Least Common Multiple (LCM) of 59 and 200
The least common multiple (LCM) of 59 and 200 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 59 and 200?
First, calculate the GCD of 59 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 200 = 0 remainder 59 |
| 2 | 200 ÷ 59 = 3 remainder 23 |
| 3 | 59 ÷ 23 = 2 remainder 13 |
| 4 | 23 ÷ 13 = 1 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 10 | 120 |
| 120 and 94 | 5640 |
| 70 and 25 | 350 |
| 144 and 22 | 1584 |
| 130 and 175 | 4550 |