Least Common Multiple (LCM) of 117 and 197
The least common multiple (LCM) of 117 and 197 is 23049.
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 117 and 197?
First, calculate the GCD of 117 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 197 = 0 remainder 117 |
| 2 | 197 ÷ 117 = 1 remainder 80 |
| 3 | 117 ÷ 80 = 1 remainder 37 |
| 4 | 80 ÷ 37 = 2 remainder 6 |
| 5 | 37 ÷ 6 = 6 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 167 | 10688 |
| 45 and 78 | 1170 |
| 158 and 196 | 15484 |
| 158 and 138 | 10902 |
| 22 and 169 | 3718 |