Least Common Multiple (LCM) of 115 and 187
The least common multiple (LCM) of 115 and 187 is 21505.
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 115 and 187?
First, calculate the GCD of 115 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 187 = 0 remainder 115 |
| 2 | 187 ÷ 115 = 1 remainder 72 |
| 3 | 115 ÷ 72 = 1 remainder 43 |
| 4 | 72 ÷ 43 = 1 remainder 29 |
| 5 | 43 ÷ 29 = 1 remainder 14 |
| 6 | 29 ÷ 14 = 2 remainder 1 |
| 7 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 30 | 300 |
| 122 and 98 | 5978 |
| 29 and 96 | 2784 |
| 35 and 131 | 4585 |
| 38 and 83 | 3154 |