Least Common Multiple (LCM) of 197 and 121
The least common multiple (LCM) of 197 and 121 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 197 and 121?
First, calculate the GCD of 197 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 121 = 1 remainder 76 |
| 2 | 121 ÷ 76 = 1 remainder 45 |
| 3 | 76 ÷ 45 = 1 remainder 31 |
| 4 | 45 ÷ 31 = 1 remainder 14 |
| 5 | 31 ÷ 14 = 2 remainder 3 |
| 6 | 14 ÷ 3 = 4 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 147 | 16170 |
| 114 and 103 | 11742 |
| 94 and 50 | 2350 |
| 94 and 61 | 5734 |
| 185 and 163 | 30155 |