Least Common Multiple (LCM) of 189 and 15
The least common multiple (LCM) of 189 and 15 is 945.
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 15?
First, calculate the GCD of 189 and 15 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 15 = 12 remainder 9 |
| 2 | 15 ÷ 9 = 1 remainder 6 |
| 3 | 9 ÷ 6 = 1 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 51 | 5610 |
| 111 and 74 | 222 |
| 136 and 76 | 2584 |
| 51 and 147 | 2499 |
| 49 and 154 | 1078 |