Least Common Multiple (LCM) of 115 and 72
The least common multiple (LCM) of 115 and 72 is 8280.
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 72?
First, calculate the GCD of 115 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 72 = 1 remainder 43 |
| 2 | 72 ÷ 43 = 1 remainder 29 |
| 3 | 43 ÷ 29 = 1 remainder 14 |
| 4 | 29 ÷ 14 = 2 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 199 | 13532 |
| 171 and 87 | 4959 |
| 65 and 154 | 10010 |
| 131 and 165 | 21615 |
| 107 and 200 | 21400 |