Least Common Multiple (LCM) of 135 and 192
The least common multiple (LCM) of 135 and 192 is 8640.
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 192?
First, calculate the GCD of 135 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 192 = 0 remainder 135 |
| 2 | 192 ÷ 135 = 1 remainder 57 |
| 3 | 135 ÷ 57 = 2 remainder 21 |
| 4 | 57 ÷ 21 = 2 remainder 15 |
| 5 | 21 ÷ 15 = 1 remainder 6 |
| 6 | 15 ÷ 6 = 2 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 57 | 4731 |
| 34 and 17 | 34 |
| 155 and 99 | 15345 |
| 117 and 195 | 585 |
| 123 and 102 | 4182 |