Least Common Multiple (LCM) of 199 and 135
The least common multiple (LCM) of 199 and 135 is 26865.
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 199 and 135?
First, calculate the GCD of 199 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 135 = 1 remainder 64 |
| 2 | 135 ÷ 64 = 2 remainder 7 |
| 3 | 64 ÷ 7 = 9 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 19 | 1349 |
| 129 and 45 | 1935 |
| 89 and 154 | 13706 |
| 56 and 190 | 5320 |
| 54 and 195 | 3510 |