Least Common Multiple (LCM) of 100 and 83
The least common multiple (LCM) of 100 and 83 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 100 and 83?
First, calculate the GCD of 100 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 83 = 1 remainder 17 |
| 2 | 83 ÷ 17 = 4 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 33 | 4686 |
| 110 and 112 | 6160 |
| 144 and 62 | 4464 |
| 165 and 59 | 9735 |
| 133 and 78 | 10374 |