Least Common Multiple (LCM) of 69 and 191
The least common multiple (LCM) of 69 and 191 is 13179.
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 191?
First, calculate the GCD of 69 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 191 = 0 remainder 69 |
| 2 | 191 ÷ 69 = 2 remainder 53 |
| 3 | 69 ÷ 53 = 1 remainder 16 |
| 4 | 53 ÷ 16 = 3 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 169 | 2366 |
| 83 and 136 | 11288 |
| 73 and 186 | 13578 |
| 180 and 194 | 17460 |
| 184 and 56 | 1288 |