Least Common Multiple (LCM) of 187 and 117
The least common multiple (LCM) of 187 and 117 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 187 and 117?
First, calculate the GCD of 187 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 117 = 1 remainder 70 |
| 2 | 117 ÷ 70 = 1 remainder 47 |
| 3 | 70 ÷ 47 = 1 remainder 23 |
| 4 | 47 ÷ 23 = 2 remainder 1 |
| 5 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 89 | 3115 |
| 129 and 102 | 4386 |
| 196 and 148 | 7252 |
| 172 and 89 | 15308 |
| 72 and 173 | 12456 |