Least Common Multiple (LCM) of 135 and 71
The least common multiple (LCM) of 135 and 71 is 9585.
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 71?
First, calculate the GCD of 135 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 71 = 1 remainder 64 |
| 2 | 71 ÷ 64 = 1 remainder 7 |
| 3 | 64 ÷ 7 = 9 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 82 | 3280 |
| 103 and 11 | 1133 |
| 120 and 107 | 12840 |
| 103 and 45 | 4635 |
| 55 and 167 | 9185 |