Least Common Multiple (LCM) of 59 and 89
The least common multiple (LCM) of 59 and 89 is 5251.
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 59 and 89?
First, calculate the GCD of 59 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 89 = 0 remainder 59 |
| 2 | 89 ÷ 59 = 1 remainder 30 |
| 3 | 59 ÷ 30 = 1 remainder 29 |
| 4 | 30 ÷ 29 = 1 remainder 1 |
| 5 | 29 ÷ 1 = 29 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 153 | 8415 |
| 31 and 184 | 5704 |
| 45 and 195 | 585 |
| 101 and 53 | 5353 |
| 123 and 166 | 20418 |