Least Common Multiple (LCM) of 194 and 67
The least common multiple (LCM) of 194 and 67 is 12998.
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 194 and 67?
First, calculate the GCD of 194 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 67 = 2 remainder 60 |
| 2 | 67 ÷ 60 = 1 remainder 7 |
| 3 | 60 ÷ 7 = 8 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 99 | 99 |
| 14 and 78 | 546 |
| 139 and 73 | 10147 |
| 147 and 89 | 13083 |
| 120 and 128 | 1920 |