Least Common Multiple (LCM) of 115 and 108
The least common multiple (LCM) of 115 and 108 is 12420.
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 108?
First, calculate the GCD of 115 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 108 = 1 remainder 7 |
| 2 | 108 ÷ 7 = 15 remainder 3 |
| 3 | 7 ÷ 3 = 2 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 90 | 10710 |
| 126 and 179 | 22554 |
| 88 and 30 | 1320 |
| 22 and 97 | 2134 |
| 59 and 31 | 1829 |