Least Common Multiple (LCM) of 164 and 195
The least common multiple (LCM) of 164 and 195 is 31980.
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 195?
First, calculate the GCD of 164 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 195 = 0 remainder 164 |
| 2 | 195 ÷ 164 = 1 remainder 31 |
| 3 | 164 ÷ 31 = 5 remainder 9 |
| 4 | 31 ÷ 9 = 3 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 24 | 48 |
| 33 and 138 | 1518 |
| 94 and 67 | 6298 |
| 64 and 113 | 7232 |
| 112 and 82 | 4592 |