Least Common Multiple (LCM) of 50 and 81
The least common multiple (LCM) of 50 and 81 is 4050.
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 81?
First, calculate the GCD of 50 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 81 = 0 remainder 50 |
| 2 | 81 ÷ 50 = 1 remainder 31 |
| 3 | 50 ÷ 31 = 1 remainder 19 |
| 4 | 31 ÷ 19 = 1 remainder 12 |
| 5 | 19 ÷ 12 = 1 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 52 | 4004 |
| 24 and 122 | 1464 |
| 51 and 60 | 1020 |
| 189 and 78 | 4914 |
| 88 and 181 | 15928 |