Least Common Multiple (LCM) of 135 and 36
The least common multiple (LCM) of 135 and 36 is 540.
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 36?
First, calculate the GCD of 135 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 36 = 3 remainder 27 |
| 2 | 36 ÷ 27 = 1 remainder 9 |
| 3 | 27 ÷ 9 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 75 | 14100 |
| 83 and 164 | 13612 |
| 68 and 104 | 1768 |
| 106 and 123 | 13038 |
| 108 and 57 | 2052 |