Least Common Multiple (LCM) of 135 and 58
The least common multiple (LCM) of 135 and 58 is 7830.
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 58?
First, calculate the GCD of 135 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 58 = 2 remainder 19 |
| 2 | 58 ÷ 19 = 3 remainder 1 |
| 3 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 180 | 180 |
| 124 and 138 | 8556 |
| 113 and 91 | 10283 |
| 145 and 99 | 14355 |
| 87 and 65 | 5655 |