Least Common Multiple (LCM) of 197 and 117
The least common multiple (LCM) of 197 and 117 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 197 and 117?
First, calculate the GCD of 197 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 117 = 1 remainder 80 |
| 2 | 117 ÷ 80 = 1 remainder 37 |
| 3 | 80 ÷ 37 = 2 remainder 6 |
| 4 | 37 ÷ 6 = 6 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 180 | 1980 |
| 63 and 72 | 504 |
| 145 and 131 | 18995 |
| 150 and 142 | 10650 |
| 15 and 127 | 1905 |