Least Common Multiple (LCM) of 187 and 108
The least common multiple (LCM) of 187 and 108 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 187 and 108?
First, calculate the GCD of 187 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 108 = 1 remainder 79 |
| 2 | 108 ÷ 79 = 1 remainder 29 |
| 3 | 79 ÷ 29 = 2 remainder 21 |
| 4 | 29 ÷ 21 = 1 remainder 8 |
| 5 | 21 ÷ 8 = 2 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 61 | 10187 |
| 174 and 140 | 12180 |
| 108 and 162 | 324 |
| 99 and 82 | 8118 |
| 131 and 54 | 7074 |