Least Common Multiple (LCM) of 162 and 85
The least common multiple (LCM) of 162 and 85 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 162 and 85?
First, calculate the GCD of 162 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 85 = 1 remainder 77 |
| 2 | 85 ÷ 77 = 1 remainder 8 |
| 3 | 77 ÷ 8 = 9 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 14 | 1694 |
| 15 and 42 | 210 |
| 175 and 42 | 1050 |
| 139 and 128 | 17792 |
| 67 and 16 | 1072 |