Least Common Multiple (LCM) of 89 and 162
The least common multiple (LCM) of 89 and 162 is 14418.
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 162?
First, calculate the GCD of 89 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 162 = 0 remainder 89 |
| 2 | 162 ÷ 89 = 1 remainder 73 |
| 3 | 89 ÷ 73 = 1 remainder 16 |
| 4 | 73 ÷ 16 = 4 remainder 9 |
| 5 | 16 ÷ 9 = 1 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 23 | 874 |
| 185 and 17 | 3145 |
| 188 and 35 | 6580 |
| 199 and 63 | 12537 |
| 164 and 99 | 16236 |