Least Common Multiple (LCM) of 164 and 89
The least common multiple (LCM) of 164 and 89 is 14596.
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 164 and 89?
First, calculate the GCD of 164 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 89 = 1 remainder 75 |
| 2 | 89 ÷ 75 = 1 remainder 14 |
| 3 | 75 ÷ 14 = 5 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 105 | 10920 |
| 97 and 14 | 1358 |
| 181 and 57 | 10317 |
| 138 and 48 | 1104 |
| 121 and 67 | 8107 |