Least Common Multiple (LCM) of 107 and 200
The least common multiple (LCM) of 107 and 200 is 21400.
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 107 and 200?
First, calculate the GCD of 107 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 200 = 0 remainder 107 |
| 2 | 200 ÷ 107 = 1 remainder 93 |
| 3 | 107 ÷ 93 = 1 remainder 14 |
| 4 | 93 ÷ 14 = 6 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 187 | 19261 |
| 105 and 80 | 1680 |
| 32 and 198 | 3168 |
| 197 and 63 | 12411 |
| 158 and 56 | 4424 |