Least Common Multiple (LCM) of 135 and 73
The least common multiple (LCM) of 135 and 73 is 9855.
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 73?
First, calculate the GCD of 135 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 73 = 1 remainder 62 |
| 2 | 73 ÷ 62 = 1 remainder 11 |
| 3 | 62 ÷ 11 = 5 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 69 | 1863 |
| 37 and 195 | 7215 |
| 20 and 187 | 3740 |
| 185 and 187 | 34595 |
| 63 and 129 | 2709 |