Least Common Multiple (LCM) of 102 and 189
The least common multiple (LCM) of 102 and 189 is 6426.
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 102 and 189?
First, calculate the GCD of 102 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 189 = 0 remainder 102 |
| 2 | 189 ÷ 102 = 1 remainder 87 |
| 3 | 102 ÷ 87 = 1 remainder 15 |
| 4 | 87 ÷ 15 = 5 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 178 | 14952 |
| 180 and 104 | 4680 |
| 59 and 115 | 6785 |
| 185 and 79 | 14615 |
| 157 and 62 | 9734 |