Least Common Multiple (LCM) of 187 and 115
The least common multiple (LCM) of 187 and 115 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 187 and 115?
First, calculate the GCD of 187 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 115 = 1 remainder 72 |
| 2 | 115 ÷ 72 = 1 remainder 43 |
| 3 | 72 ÷ 43 = 1 remainder 29 |
| 4 | 43 ÷ 29 = 1 remainder 14 |
| 5 | 29 ÷ 14 = 2 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 132 | 13596 |
| 192 and 176 | 2112 |
| 153 and 111 | 5661 |
| 75 and 153 | 3825 |
| 117 and 159 | 6201 |