Least Common Multiple (LCM) of 30 and 115
The least common multiple (LCM) of 30 and 115 is 690.
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 30 and 115?
First, calculate the GCD of 30 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 115 = 0 remainder 30 |
| 2 | 115 ÷ 30 = 3 remainder 25 |
| 3 | 30 ÷ 25 = 1 remainder 5 |
| 4 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 124 | 5828 |
| 185 and 131 | 24235 |
| 154 and 100 | 7700 |
| 147 and 122 | 17934 |
| 110 and 137 | 15070 |