Least Common Multiple (LCM) of 189 and 79
The least common multiple (LCM) of 189 and 79 is 14931.
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 189 and 79?
First, calculate the GCD of 189 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 79 = 2 remainder 31 |
| 2 | 79 ÷ 31 = 2 remainder 17 |
| 3 | 31 ÷ 17 = 1 remainder 14 |
| 4 | 17 ÷ 14 = 1 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 169 | 29913 |
| 29 and 13 | 377 |
| 106 and 131 | 13886 |
| 116 and 114 | 6612 |
| 85 and 169 | 14365 |