Least Common Multiple (LCM) of 135 and 65
The least common multiple (LCM) of 135 and 65 is 1755.
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 65?
First, calculate the GCD of 135 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 65 = 2 remainder 5 |
| 2 | 65 ÷ 5 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 13 | 1664 |
| 107 and 82 | 8774 |
| 68 and 134 | 4556 |
| 128 and 117 | 14976 |
| 172 and 137 | 23564 |