Least Common Multiple (LCM) of 135 and 194
The least common multiple (LCM) of 135 and 194 is 26190.
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 194?
First, calculate the GCD of 135 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 194 = 0 remainder 135 |
| 2 | 194 ÷ 135 = 1 remainder 59 |
| 3 | 135 ÷ 59 = 2 remainder 17 |
| 4 | 59 ÷ 17 = 3 remainder 8 |
| 5 | 17 ÷ 8 = 2 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 154 | 1232 |
| 157 and 97 | 15229 |
| 158 and 54 | 4266 |
| 107 and 10 | 1070 |
| 129 and 14 | 1806 |