Least Common Multiple (LCM) of 100 and 183
The least common multiple (LCM) of 100 and 183 is 18300.
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 183?
First, calculate the GCD of 100 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 183 = 0 remainder 100 |
| 2 | 183 ÷ 100 = 1 remainder 83 |
| 3 | 100 ÷ 83 = 1 remainder 17 |
| 4 | 83 ÷ 17 = 4 remainder 15 |
| 5 | 17 ÷ 15 = 1 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 199 | 18109 |
| 144 and 150 | 3600 |
| 39 and 133 | 5187 |
| 38 and 173 | 6574 |
| 129 and 120 | 5160 |