Least Common Multiple (LCM) of 83 and 51
The least common multiple (LCM) of 83 and 51 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 83 and 51?
First, calculate the GCD of 83 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 51 = 1 remainder 32 |
| 2 | 51 ÷ 32 = 1 remainder 19 |
| 3 | 32 ÷ 19 = 1 remainder 13 |
| 4 | 19 ÷ 13 = 1 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 89 | 17088 |
| 12 and 133 | 1596 |
| 174 and 171 | 9918 |
| 104 and 56 | 728 |
| 197 and 195 | 38415 |