Least Common Multiple (LCM) of 119 and 193
The least common multiple (LCM) of 119 and 193 is 22967.
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 119 and 193?
First, calculate the GCD of 119 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 193 = 0 remainder 119 |
| 2 | 193 ÷ 119 = 1 remainder 74 |
| 3 | 119 ÷ 74 = 1 remainder 45 |
| 4 | 74 ÷ 45 = 1 remainder 29 |
| 5 | 45 ÷ 29 = 1 remainder 16 |
| 6 | 29 ÷ 16 = 1 remainder 13 |
| 7 | 16 ÷ 13 = 1 remainder 3 |
| 8 | 13 ÷ 3 = 4 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 61 | 9699 |
| 133 and 149 | 19817 |
| 45 and 188 | 8460 |
| 106 and 112 | 5936 |
| 53 and 186 | 9858 |