Least Common Multiple (LCM) of 78 and 187
The least common multiple (LCM) of 78 and 187 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 78 and 187?
First, calculate the GCD of 78 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 187 = 0 remainder 78 |
| 2 | 187 ÷ 78 = 2 remainder 31 |
| 3 | 78 ÷ 31 = 2 remainder 16 |
| 4 | 31 ÷ 16 = 1 remainder 15 |
| 5 | 16 ÷ 15 = 1 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 12 | 1596 |
| 32 and 128 | 128 |
| 117 and 187 | 21879 |
| 147 and 18 | 882 |
| 161 and 166 | 26726 |