Least Common Multiple (LCM) of 115 and 120
The least common multiple (LCM) of 115 and 120 is 2760.
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 120?
First, calculate the GCD of 115 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 120 = 0 remainder 115 |
| 2 | 120 ÷ 115 = 1 remainder 5 |
| 3 | 115 ÷ 5 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 106 | 5300 |
| 36 and 88 | 792 |
| 122 and 21 | 2562 |
| 13 and 147 | 1911 |
| 58 and 173 | 10034 |