Least Common Multiple (LCM) of 135 and 32
The least common multiple (LCM) of 135 and 32 is 4320.
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 32?
First, calculate the GCD of 135 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 32 = 4 remainder 7 |
| 2 | 32 ÷ 7 = 4 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 184 | 4416 |
| 144 and 20 | 720 |
| 53 and 50 | 2650 |
| 31 and 107 | 3317 |
| 89 and 56 | 4984 |