Least Common Multiple (LCM) of 89 and 160
The least common multiple (LCM) of 89 and 160 is 14240.
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 89 and 160?
First, calculate the GCD of 89 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 160 = 0 remainder 89 |
| 2 | 160 ÷ 89 = 1 remainder 71 |
| 3 | 89 ÷ 71 = 1 remainder 18 |
| 4 | 71 ÷ 18 = 3 remainder 17 |
| 5 | 18 ÷ 17 = 1 remainder 1 |
| 6 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 35 | 945 |
| 196 and 107 | 20972 |
| 147 and 36 | 1764 |
| 135 and 73 | 9855 |
| 83 and 55 | 4565 |