Least Common Multiple (LCM) of 115 and 156
The least common multiple (LCM) of 115 and 156 is 17940.
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 156?
First, calculate the GCD of 115 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 156 = 0 remainder 115 |
| 2 | 156 ÷ 115 = 1 remainder 41 |
| 3 | 115 ÷ 41 = 2 remainder 33 |
| 4 | 41 ÷ 33 = 1 remainder 8 |
| 5 | 33 ÷ 8 = 4 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 74 | 5106 |
| 110 and 22 | 110 |
| 30 and 173 | 5190 |
| 25 and 75 | 75 |
| 175 and 80 | 2800 |