Least Common Multiple (LCM) of 200 and 106
The least common multiple (LCM) of 200 and 106 is 10600.
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 106?
First, calculate the GCD of 200 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 106 = 1 remainder 94 |
| 2 | 106 ÷ 94 = 1 remainder 12 |
| 3 | 94 ÷ 12 = 7 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 128 | 2688 |
| 15 and 182 | 2730 |
| 88 and 186 | 8184 |
| 177 and 111 | 6549 |
| 33 and 61 | 2013 |