Least Common Multiple (LCM) of 102 and 197
The least common multiple (LCM) of 102 and 197 is 20094.
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 102 and 197?
First, calculate the GCD of 102 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 197 = 0 remainder 102 |
| 2 | 197 ÷ 102 = 1 remainder 95 |
| 3 | 102 ÷ 95 = 1 remainder 7 |
| 4 | 95 ÷ 7 = 13 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 140 | 700 |
| 162 and 119 | 19278 |
| 13 and 115 | 1495 |
| 54 and 91 | 4914 |
| 63 and 108 | 756 |