Least Common Multiple (LCM) of 51 and 83
The least common multiple (LCM) of 51 and 83 is 4233.
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 51 and 83?
First, calculate the GCD of 51 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 83 = 0 remainder 51 |
| 2 | 83 ÷ 51 = 1 remainder 32 |
| 3 | 51 ÷ 32 = 1 remainder 19 |
| 4 | 32 ÷ 19 = 1 remainder 13 |
| 5 | 19 ÷ 13 = 1 remainder 6 |
| 6 | 13 ÷ 6 = 2 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 65 | 12740 |
| 154 and 33 | 462 |
| 125 and 85 | 2125 |
| 18 and 104 | 936 |
| 149 and 83 | 12367 |