Least Common Multiple (LCM) of 85 and 162
The least common multiple (LCM) of 85 and 162 is 13770.
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 85 and 162?
First, calculate the GCD of 85 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 162 = 0 remainder 85 |
| 2 | 162 ÷ 85 = 1 remainder 77 |
| 3 | 85 ÷ 77 = 1 remainder 8 |
| 4 | 77 ÷ 8 = 9 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 45 | 1845 |
| 87 and 71 | 6177 |
| 30 and 71 | 2130 |
| 165 and 192 | 10560 |
| 108 and 110 | 5940 |