Least Common Multiple (LCM) of 106 and 200
The least common multiple (LCM) of 106 and 200 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 106 and 200?
First, calculate the GCD of 106 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 200 = 0 remainder 106 |
| 2 | 200 ÷ 106 = 1 remainder 94 |
| 3 | 106 ÷ 94 = 1 remainder 12 |
| 4 | 94 ÷ 12 = 7 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 164 | 11644 |
| 90 and 159 | 4770 |
| 33 and 14 | 462 |
| 112 and 93 | 10416 |
| 144 and 122 | 8784 |