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 |
|---|---|
| 142 and 64 | 4544 |
| 146 and 70 | 5110 |
| 166 and 65 | 10790 |
| 191 and 10 | 1910 |
| 159 and 98 | 15582 |