Least Common Multiple (LCM) of 115 and 168
The least common multiple (LCM) of 115 and 168 is 19320.
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 168?
First, calculate the GCD of 115 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 168 = 0 remainder 115 |
| 2 | 168 ÷ 115 = 1 remainder 53 |
| 3 | 115 ÷ 53 = 2 remainder 9 |
| 4 | 53 ÷ 9 = 5 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 35 | 525 |
| 122 and 93 | 11346 |
| 29 and 86 | 2494 |
| 137 and 12 | 1644 |
| 172 and 37 | 6364 |