Least Common Multiple (LCM) of 115 and 74
The least common multiple (LCM) of 115 and 74 is 8510.
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 74?
First, calculate the GCD of 115 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 74 = 1 remainder 41 |
| 2 | 74 ÷ 41 = 1 remainder 33 |
| 3 | 41 ÷ 33 = 1 remainder 8 |
| 4 | 33 ÷ 8 = 4 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 111 | 8103 |
| 179 and 124 | 22196 |
| 184 and 103 | 18952 |
| 200 and 133 | 26600 |
| 198 and 25 | 4950 |