Least Common Multiple (LCM) of 58 and 89
The least common multiple (LCM) of 58 and 89 is 5162.
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 58 and 89?
First, calculate the GCD of 58 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 89 = 0 remainder 58 |
| 2 | 89 ÷ 58 = 1 remainder 31 |
| 3 | 58 ÷ 31 = 1 remainder 27 |
| 4 | 31 ÷ 27 = 1 remainder 4 |
| 5 | 27 ÷ 4 = 6 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 120 | 8760 |
| 194 and 135 | 26190 |
| 42 and 123 | 1722 |
| 40 and 194 | 3880 |
| 160 and 14 | 1120 |