Least Common Multiple (LCM) of 164 and 193
The least common multiple (LCM) of 164 and 193 is 31652.
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 193?
First, calculate the GCD of 164 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 193 = 0 remainder 164 |
| 2 | 193 ÷ 164 = 1 remainder 29 |
| 3 | 164 ÷ 29 = 5 remainder 19 |
| 4 | 29 ÷ 19 = 1 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 180 | 720 |
| 131 and 72 | 9432 |
| 32 and 182 | 2912 |
| 44 and 165 | 660 |
| 65 and 93 | 6045 |