Least Common Multiple (LCM) of 200 and 108
The least common multiple (LCM) of 200 and 108 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 200 and 108?
First, calculate the GCD of 200 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 108 = 1 remainder 92 |
| 2 | 108 ÷ 92 = 1 remainder 16 |
| 3 | 92 ÷ 16 = 5 remainder 12 |
| 4 | 16 ÷ 12 = 1 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 22 | 264 |
| 37 and 116 | 4292 |
| 62 and 113 | 7006 |
| 108 and 91 | 9828 |
| 29 and 61 | 1769 |