Least Common Multiple (LCM) of 187 and 69
The least common multiple (LCM) of 187 and 69 is 12903.
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 187 and 69?
First, calculate the GCD of 187 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 69 = 2 remainder 49 |
| 2 | 69 ÷ 49 = 1 remainder 20 |
| 3 | 49 ÷ 20 = 2 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 180 | 1980 |
| 95 and 138 | 13110 |
| 138 and 148 | 10212 |
| 50 and 68 | 1700 |
| 49 and 109 | 5341 |