Least Common Multiple (LCM) of 73 and 115
The least common multiple (LCM) of 73 and 115 is 8395.
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 73 and 115?
First, calculate the GCD of 73 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 115 = 0 remainder 73 |
| 2 | 115 ÷ 73 = 1 remainder 42 |
| 3 | 73 ÷ 42 = 1 remainder 31 |
| 4 | 42 ÷ 31 = 1 remainder 11 |
| 5 | 31 ÷ 11 = 2 remainder 9 |
| 6 | 11 ÷ 9 = 1 remainder 2 |
| 7 | 9 ÷ 2 = 4 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 14 | 826 |
| 108 and 61 | 6588 |
| 97 and 90 | 8730 |
| 17 and 37 | 629 |
| 170 and 199 | 33830 |