Least Common Multiple (LCM) of 135 and 64
The least common multiple (LCM) of 135 and 64 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 64?
First, calculate the GCD of 135 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 64 = 2 remainder 7 |
| 2 | 64 ÷ 7 = 9 remainder 1 |
| 3 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 11 | 1056 |
| 54 and 30 | 270 |
| 49 and 142 | 6958 |
| 77 and 187 | 1309 |
| 64 and 151 | 9664 |