Least Common Multiple (LCM) of 108 and 185
The least common multiple (LCM) of 108 and 185 is 19980.
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 185?
First, calculate the GCD of 108 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 185 = 0 remainder 108 |
| 2 | 185 ÷ 108 = 1 remainder 77 |
| 3 | 108 ÷ 77 = 1 remainder 31 |
| 4 | 77 ÷ 31 = 2 remainder 15 |
| 5 | 31 ÷ 15 = 2 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 91 | 1456 |
| 108 and 33 | 1188 |
| 59 and 152 | 8968 |
| 89 and 37 | 3293 |
| 16 and 184 | 368 |