Least Common Multiple (LCM) of 85 and 164
The least common multiple (LCM) of 85 and 164 is 13940.
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 164?
First, calculate the GCD of 85 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 164 = 0 remainder 85 |
| 2 | 164 ÷ 85 = 1 remainder 79 |
| 3 | 85 ÷ 79 = 1 remainder 6 |
| 4 | 79 ÷ 6 = 13 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 69 | 4140 |
| 60 and 88 | 1320 |
| 156 and 75 | 3900 |
| 196 and 40 | 1960 |
| 154 and 23 | 3542 |