Least Common Multiple (LCM) of 108 and 133
The least common multiple (LCM) of 108 and 133 is 14364.
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 133?
First, calculate the GCD of 108 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 133 = 0 remainder 108 |
| 2 | 133 ÷ 108 = 1 remainder 25 |
| 3 | 108 ÷ 25 = 4 remainder 8 |
| 4 | 25 ÷ 8 = 3 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 86 | 2666 |
| 193 and 28 | 5404 |
| 110 and 166 | 9130 |
| 123 and 200 | 24600 |
| 118 and 13 | 1534 |