Least Common Multiple (LCM) of 135 and 111
The least common multiple (LCM) of 135 and 111 is 4995.
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 111?
First, calculate the GCD of 135 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 111 = 1 remainder 24 |
| 2 | 111 ÷ 24 = 4 remainder 15 |
| 3 | 24 ÷ 15 = 1 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 135 | 8370 |
| 54 and 17 | 918 |
| 102 and 26 | 1326 |
| 199 and 107 | 21293 |
| 61 and 42 | 2562 |