Least Common Multiple (LCM) of 117 and 187
The least common multiple (LCM) of 117 and 187 is 21879.
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 117 and 187?
First, calculate the GCD of 117 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 187 = 0 remainder 117 |
| 2 | 187 ÷ 117 = 1 remainder 70 |
| 3 | 117 ÷ 70 = 1 remainder 47 |
| 4 | 70 ÷ 47 = 1 remainder 23 |
| 5 | 47 ÷ 23 = 2 remainder 1 |
| 6 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 21 | 105 |
| 197 and 35 | 6895 |
| 136 and 136 | 136 |
| 60 and 144 | 720 |
| 131 and 157 | 20567 |