Least Common Multiple (LCM) of 83 and 100
The least common multiple (LCM) of 83 and 100 is 8300.
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 100?
First, calculate the GCD of 83 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 100 = 0 remainder 83 |
| 2 | 100 ÷ 83 = 1 remainder 17 |
| 3 | 83 ÷ 17 = 4 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 11 | 1155 |
| 128 and 185 | 23680 |
| 144 and 158 | 11376 |
| 188 and 11 | 2068 |
| 38 and 51 | 1938 |