Least Common Multiple (LCM) of 69 and 194
The least common multiple (LCM) of 69 and 194 is 13386.
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 69 and 194?
First, calculate the GCD of 69 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 194 = 0 remainder 69 |
| 2 | 194 ÷ 69 = 2 remainder 56 |
| 3 | 69 ÷ 56 = 1 remainder 13 |
| 4 | 56 ÷ 13 = 4 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 81 | 11745 |
| 122 and 133 | 16226 |
| 25 and 82 | 2050 |
| 114 and 77 | 8778 |
| 169 and 47 | 7943 |