Least Common Multiple (LCM) of 49 and 115
The least common multiple (LCM) of 49 and 115 is 5635.
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 49 and 115?
First, calculate the GCD of 49 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 115 = 0 remainder 49 |
| 2 | 115 ÷ 49 = 2 remainder 17 |
| 3 | 49 ÷ 17 = 2 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 115 | 18170 |
| 119 and 83 | 9877 |
| 112 and 82 | 4592 |
| 45 and 162 | 810 |
| 26 and 61 | 1586 |