Least Common Multiple (LCM) of 135 and 199
The least common multiple (LCM) of 135 and 199 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 135 and 199?
First, calculate the GCD of 135 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 199 = 0 remainder 135 |
| 2 | 199 ÷ 135 = 1 remainder 64 |
| 3 | 135 ÷ 64 = 2 remainder 7 |
| 4 | 64 ÷ 7 = 9 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 79 | 6399 |
| 194 and 165 | 32010 |
| 128 and 72 | 1152 |
| 44 and 25 | 1100 |
| 113 and 118 | 13334 |