Least Common Multiple (LCM) of 164 and 85
The least common multiple (LCM) of 164 and 85 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 164 and 85?
First, calculate the GCD of 164 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 85 = 1 remainder 79 |
| 2 | 85 ÷ 79 = 1 remainder 6 |
| 3 | 79 ÷ 6 = 13 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 62 | 2108 |
| 170 and 188 | 15980 |
| 62 and 113 | 7006 |
| 172 and 39 | 6708 |
| 159 and 129 | 6837 |