Least Common Multiple (LCM) of 193 and 119
The least common multiple (LCM) of 193 and 119 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 193 and 119?
First, calculate the GCD of 193 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 119 = 1 remainder 74 |
| 2 | 119 ÷ 74 = 1 remainder 45 |
| 3 | 74 ÷ 45 = 1 remainder 29 |
| 4 | 45 ÷ 29 = 1 remainder 16 |
| 5 | 29 ÷ 16 = 1 remainder 13 |
| 6 | 16 ÷ 13 = 1 remainder 3 |
| 7 | 13 ÷ 3 = 4 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 188 | 22748 |
| 160 and 128 | 640 |
| 34 and 162 | 2754 |
| 35 and 35 | 35 |
| 112 and 182 | 1456 |