Least Common Multiple (LCM) of 135 and 158
The least common multiple (LCM) of 135 and 158 is 21330.
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 158?
First, calculate the GCD of 135 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 158 = 0 remainder 135 |
| 2 | 158 ÷ 135 = 1 remainder 23 |
| 3 | 135 ÷ 23 = 5 remainder 20 |
| 4 | 23 ÷ 20 = 1 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 75 | 675 |
| 56 and 49 | 392 |
| 194 and 32 | 3104 |
| 137 and 80 | 10960 |
| 49 and 121 | 5929 |