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 |
|---|---|
| 190 and 140 | 2660 |
| 13 and 119 | 1547 |
| 45 and 150 | 450 |
| 158 and 85 | 13430 |
| 115 and 10 | 230 |