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 |
|---|---|
| 129 and 105 | 4515 |
| 174 and 50 | 4350 |
| 157 and 85 | 13345 |
| 127 and 177 | 22479 |
| 188 and 146 | 13724 |