Least Common Multiple (LCM) of 135 and 160
The least common multiple (LCM) of 135 and 160 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 160?
First, calculate the GCD of 135 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 160 = 0 remainder 135 |
| 2 | 160 ÷ 135 = 1 remainder 25 |
| 3 | 135 ÷ 25 = 5 remainder 10 |
| 4 | 25 ÷ 10 = 2 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 14 | 2758 |
| 159 and 18 | 954 |
| 154 and 66 | 462 |
| 181 and 33 | 5973 |
| 135 and 32 | 4320 |