Least Common Multiple (LCM) of 135 and 93
The least common multiple (LCM) of 135 and 93 is 4185.
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 93?
First, calculate the GCD of 135 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 93 = 1 remainder 42 |
| 2 | 93 ÷ 42 = 2 remainder 9 |
| 3 | 42 ÷ 9 = 4 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 60 | 1860 |
| 109 and 49 | 5341 |
| 123 and 124 | 15252 |
| 167 and 164 | 27388 |
| 177 and 169 | 29913 |