Least Common Multiple (LCM) of 115 and 100
The least common multiple (LCM) of 115 and 100 is 2300.
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 100?
First, calculate the GCD of 115 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 100 = 1 remainder 15 |
| 2 | 100 ÷ 15 = 6 remainder 10 |
| 3 | 15 ÷ 10 = 1 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 104 | 312 |
| 86 and 122 | 5246 |
| 46 and 164 | 3772 |
| 127 and 144 | 18288 |
| 107 and 63 | 6741 |