Least Common Multiple (LCM) of 108 and 197
The least common multiple (LCM) of 108 and 197 is 21276.
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 197?
First, calculate the GCD of 108 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 197 = 0 remainder 108 |
| 2 | 197 ÷ 108 = 1 remainder 89 |
| 3 | 108 ÷ 89 = 1 remainder 19 |
| 4 | 89 ÷ 19 = 4 remainder 13 |
| 5 | 19 ÷ 13 = 1 remainder 6 |
| 6 | 13 ÷ 6 = 2 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 90 | 4770 |
| 106 and 138 | 7314 |
| 113 and 126 | 14238 |
| 50 and 155 | 1550 |
| 117 and 50 | 5850 |