Least Common Multiple (LCM) of 189 and 58
The least common multiple (LCM) of 189 and 58 is 10962.
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 58?
First, calculate the GCD of 189 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 58 = 3 remainder 15 |
| 2 | 58 ÷ 15 = 3 remainder 13 |
| 3 | 15 ÷ 13 = 1 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 175 | 24675 |
| 87 and 192 | 5568 |
| 95 and 81 | 7695 |
| 74 and 113 | 8362 |
| 199 and 175 | 34825 |