Least Common Multiple (LCM) of 162 and 89
The least common multiple (LCM) of 162 and 89 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 162 and 89?
First, calculate the GCD of 162 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 89 = 1 remainder 73 |
| 2 | 89 ÷ 73 = 1 remainder 16 |
| 3 | 73 ÷ 16 = 4 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 165 | 330 |
| 107 and 11 | 1177 |
| 159 and 140 | 22260 |
| 188 and 92 | 4324 |
| 46 and 21 | 966 |