Least Common Multiple (LCM) of 115 and 73
The least common multiple (LCM) of 115 and 73 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 115 and 73?
First, calculate the GCD of 115 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 73 = 1 remainder 42 |
| 2 | 73 ÷ 42 = 1 remainder 31 |
| 3 | 42 ÷ 31 = 1 remainder 11 |
| 4 | 31 ÷ 11 = 2 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 74 | 5180 |
| 174 and 10 | 870 |
| 138 and 113 | 15594 |
| 106 and 99 | 10494 |
| 122 and 129 | 15738 |