Least Common Multiple (LCM) of 50 and 89
The least common multiple (LCM) of 50 and 89 is 4450.
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 50 and 89?
First, calculate the GCD of 50 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 89 = 0 remainder 50 |
| 2 | 89 ÷ 50 = 1 remainder 39 |
| 3 | 50 ÷ 39 = 1 remainder 11 |
| 4 | 39 ÷ 11 = 3 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 12 | 2004 |
| 168 and 13 | 2184 |
| 138 and 89 | 12282 |
| 144 and 41 | 5904 |
| 149 and 103 | 15347 |