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 |
|---|---|
| 106 and 117 | 12402 |
| 190 and 74 | 7030 |
| 112 and 174 | 9744 |
| 155 and 72 | 11160 |
| 166 and 177 | 29382 |