Least Common Multiple (LCM) of 69 and 187
The least common multiple (LCM) of 69 and 187 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 69 and 187?
First, calculate the GCD of 69 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 187 = 0 remainder 69 |
| 2 | 187 ÷ 69 = 2 remainder 49 |
| 3 | 69 ÷ 49 = 1 remainder 20 |
| 4 | 49 ÷ 20 = 2 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 196 | 8624 |
| 32 and 185 | 5920 |
| 137 and 71 | 9727 |
| 97 and 75 | 7275 |
| 150 and 83 | 12450 |