Least Common Multiple (LCM) of 100 and 189
The least common multiple (LCM) of 100 and 189 is 18900.
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 189?
First, calculate the GCD of 100 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 189 = 0 remainder 100 |
| 2 | 189 ÷ 100 = 1 remainder 89 |
| 3 | 100 ÷ 89 = 1 remainder 11 |
| 4 | 89 ÷ 11 = 8 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 20 | 60 |
| 137 and 35 | 4795 |
| 104 and 189 | 19656 |
| 126 and 52 | 3276 |
| 111 and 141 | 5217 |