Least Common Multiple (LCM) of 189 and 101
The least common multiple (LCM) of 189 and 101 is 19089.
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 189 and 101?
First, calculate the GCD of 189 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 101 = 1 remainder 88 |
| 2 | 101 ÷ 88 = 1 remainder 13 |
| 3 | 88 ÷ 13 = 6 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 109 | 12753 |
| 187 and 183 | 34221 |
| 12 and 102 | 204 |
| 33 and 139 | 4587 |
| 100 and 59 | 5900 |