Least Common Multiple (LCM) of 67 and 195
The least common multiple (LCM) of 67 and 195 is 13065.
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 67 and 195?
First, calculate the GCD of 67 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 195 = 0 remainder 67 |
| 2 | 195 ÷ 67 = 2 remainder 61 |
| 3 | 67 ÷ 61 = 1 remainder 6 |
| 4 | 61 ÷ 6 = 10 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 97 | 16005 |
| 108 and 98 | 5292 |
| 106 and 58 | 3074 |
| 154 and 148 | 11396 |
| 46 and 68 | 1564 |