Least Common Multiple (LCM) of 108 and 200
The least common multiple (LCM) of 108 and 200 is 5400.
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 108 and 200?
First, calculate the GCD of 108 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 200 = 0 remainder 108 |
| 2 | 200 ÷ 108 = 1 remainder 92 |
| 3 | 108 ÷ 92 = 1 remainder 16 |
| 4 | 92 ÷ 16 = 5 remainder 12 |
| 5 | 16 ÷ 12 = 1 remainder 4 |
| 6 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 23 | 69 |
| 177 and 17 | 3009 |
| 54 and 32 | 864 |
| 20 and 52 | 260 |
| 192 and 22 | 2112 |