Least Common Multiple (LCM) of 108 and 155
The least common multiple (LCM) of 108 and 155 is 16740.
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 155?
First, calculate the GCD of 108 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 155 = 0 remainder 108 |
| 2 | 155 ÷ 108 = 1 remainder 47 |
| 3 | 108 ÷ 47 = 2 remainder 14 |
| 4 | 47 ÷ 14 = 3 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 107 | 2140 |
| 193 and 168 | 32424 |
| 17 and 117 | 1989 |
| 62 and 27 | 1674 |
| 116 and 90 | 5220 |