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 |
|---|---|
| 55 and 42 | 2310 |
| 194 and 30 | 2910 |
| 158 and 37 | 5846 |
| 172 and 78 | 6708 |
| 190 and 124 | 11780 |