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 |
|---|---|
| 104 and 128 | 1664 |
| 139 and 35 | 4865 |
| 165 and 27 | 1485 |
| 143 and 93 | 13299 |
| 117 and 145 | 16965 |