Least Common Multiple (LCM) of 108 and 55
The least common multiple (LCM) of 108 and 55 is 5940.
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 55?
First, calculate the GCD of 108 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 55 = 1 remainder 53 |
| 2 | 55 ÷ 53 = 1 remainder 2 |
| 3 | 53 ÷ 2 = 26 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 139 | 26966 |
| 119 and 89 | 10591 |
| 108 and 81 | 324 |
| 102 and 186 | 3162 |
| 177 and 120 | 7080 |