Least Common Multiple (LCM) of 55 and 108
The least common multiple (LCM) of 55 and 108 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 55 and 108?
First, calculate the GCD of 55 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 108 = 0 remainder 55 |
| 2 | 108 ÷ 55 = 1 remainder 53 |
| 3 | 55 ÷ 53 = 1 remainder 2 |
| 4 | 53 ÷ 2 = 26 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 83 | 8715 |
| 38 and 125 | 4750 |
| 162 and 85 | 13770 |
| 129 and 130 | 16770 |
| 153 and 196 | 29988 |