Least Common Multiple (LCM) of 89 and 163
The least common multiple (LCM) of 89 and 163 is 14507.
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 163?
First, calculate the GCD of 89 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 163 = 0 remainder 89 |
| 2 | 163 ÷ 89 = 1 remainder 74 |
| 3 | 89 ÷ 74 = 1 remainder 15 |
| 4 | 74 ÷ 15 = 4 remainder 14 |
| 5 | 15 ÷ 14 = 1 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 127 | 24384 |
| 11 and 115 | 1265 |
| 21 and 40 | 840 |
| 56 and 173 | 9688 |
| 30 and 64 | 960 |