Least Common Multiple (LCM) of 121 and 197
The least common multiple (LCM) of 121 and 197 is 23837.
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 121 and 197?
First, calculate the GCD of 121 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 197 = 0 remainder 121 |
| 2 | 197 ÷ 121 = 1 remainder 76 |
| 3 | 121 ÷ 76 = 1 remainder 45 |
| 4 | 76 ÷ 45 = 1 remainder 31 |
| 5 | 45 ÷ 31 = 1 remainder 14 |
| 6 | 31 ÷ 14 = 2 remainder 3 |
| 7 | 14 ÷ 3 = 4 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 199 | 29850 |
| 198 and 24 | 792 |
| 43 and 44 | 1892 |
| 165 and 82 | 13530 |
| 35 and 174 | 6090 |