Least Common Multiple (LCM) of 72 and 115
The least common multiple (LCM) of 72 and 115 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 72 and 115?
First, calculate the GCD of 72 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 115 = 0 remainder 72 |
| 2 | 115 ÷ 72 = 1 remainder 43 |
| 3 | 72 ÷ 43 = 1 remainder 29 |
| 4 | 43 ÷ 29 = 1 remainder 14 |
| 5 | 29 ÷ 14 = 2 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 27 | 135 |
| 111 and 127 | 14097 |
| 33 and 111 | 1221 |
| 65 and 39 | 195 |
| 143 and 161 | 23023 |