Least Common Multiple (LCM) of 121 and 193
The least common multiple (LCM) of 121 and 193 is 23353.
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 193?
First, calculate the GCD of 121 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 193 = 0 remainder 121 |
| 2 | 193 ÷ 121 = 1 remainder 72 |
| 3 | 121 ÷ 72 = 1 remainder 49 |
| 4 | 72 ÷ 49 = 1 remainder 23 |
| 5 | 49 ÷ 23 = 2 remainder 3 |
| 6 | 23 ÷ 3 = 7 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 31 | 3193 |
| 42 and 172 | 3612 |
| 95 and 90 | 1710 |
| 197 and 143 | 28171 |
| 112 and 58 | 3248 |