Least Common Multiple (LCM) of 119 and 198
The least common multiple (LCM) of 119 and 198 is 23562.
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 198?
First, calculate the GCD of 119 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 198 = 0 remainder 119 |
| 2 | 198 ÷ 119 = 1 remainder 79 |
| 3 | 119 ÷ 79 = 1 remainder 40 |
| 4 | 79 ÷ 40 = 1 remainder 39 |
| 5 | 40 ÷ 39 = 1 remainder 1 |
| 6 | 39 ÷ 1 = 39 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 178 | 6586 |
| 39 and 173 | 6747 |
| 198 and 72 | 792 |
| 114 and 20 | 1140 |
| 99 and 200 | 19800 |