Least Common Multiple (LCM) of 89 and 164
The least common multiple (LCM) of 89 and 164 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 89 and 164?
First, calculate the GCD of 89 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 164 = 0 remainder 89 |
| 2 | 164 ÷ 89 = 1 remainder 75 |
| 3 | 89 ÷ 75 = 1 remainder 14 |
| 4 | 75 ÷ 14 = 5 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 21 | 1407 |
| 113 and 182 | 20566 |
| 172 and 183 | 31476 |
| 21 and 153 | 1071 |
| 172 and 94 | 8084 |