Least Common Multiple (LCM) of 52 and 115
The least common multiple (LCM) of 52 and 115 is 5980.
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 52 and 115?
First, calculate the GCD of 52 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 115 = 0 remainder 52 |
| 2 | 115 ÷ 52 = 2 remainder 11 |
| 3 | 52 ÷ 11 = 4 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 65 | 2470 |
| 57 and 197 | 11229 |
| 113 and 158 | 17854 |
| 75 and 17 | 1275 |
| 120 and 78 | 1560 |