Least Common Multiple (LCM) of 119 and 194
The least common multiple (LCM) of 119 and 194 is 23086.
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 194?
First, calculate the GCD of 119 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 194 = 0 remainder 119 |
| 2 | 194 ÷ 119 = 1 remainder 75 |
| 3 | 119 ÷ 75 = 1 remainder 44 |
| 4 | 75 ÷ 44 = 1 remainder 31 |
| 5 | 44 ÷ 31 = 1 remainder 13 |
| 6 | 31 ÷ 13 = 2 remainder 5 |
| 7 | 13 ÷ 5 = 2 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 117 | 21645 |
| 80 and 120 | 240 |
| 13 and 138 | 1794 |
| 78 and 24 | 312 |
| 169 and 112 | 18928 |