Least Common Multiple (LCM) of 200 and 61
The least common multiple (LCM) of 200 and 61 is 12200.
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 61?
First, calculate the GCD of 200 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 61 = 3 remainder 17 |
| 2 | 61 ÷ 17 = 3 remainder 10 |
| 3 | 17 ÷ 10 = 1 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 94 | 9118 |
| 137 and 159 | 21783 |
| 136 and 31 | 4216 |
| 113 and 181 | 20453 |
| 120 and 25 | 600 |