Least Common Multiple (LCM) of 108 and 187
The least common multiple (LCM) of 108 and 187 is 20196.
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 187?
First, calculate the GCD of 108 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 187 = 0 remainder 108 |
| 2 | 187 ÷ 108 = 1 remainder 79 |
| 3 | 108 ÷ 79 = 1 remainder 29 |
| 4 | 79 ÷ 29 = 2 remainder 21 |
| 5 | 29 ÷ 21 = 1 remainder 8 |
| 6 | 21 ÷ 8 = 2 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 83 | 1660 |
| 129 and 95 | 12255 |
| 18 and 129 | 774 |
| 63 and 100 | 6300 |
| 110 and 80 | 880 |