Least Common Multiple (LCM) of 187 and 78
The least common multiple (LCM) of 187 and 78 is 14586.
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 78?
First, calculate the GCD of 187 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 78 = 2 remainder 31 |
| 2 | 78 ÷ 31 = 2 remainder 16 |
| 3 | 31 ÷ 16 = 1 remainder 15 |
| 4 | 16 ÷ 15 = 1 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 199 | 6169 |
| 199 and 49 | 9751 |
| 71 and 166 | 11786 |
| 41 and 30 | 1230 |
| 11 and 65 | 715 |