Least Common Multiple (LCM) of 200 and 107
The least common multiple (LCM) of 200 and 107 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 200 and 107?
First, calculate the GCD of 200 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 107 = 1 remainder 93 |
| 2 | 107 ÷ 93 = 1 remainder 14 |
| 3 | 93 ÷ 14 = 6 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 48 | 3984 |
| 63 and 144 | 1008 |
| 37 and 104 | 3848 |
| 14 and 171 | 2394 |
| 188 and 172 | 8084 |