Least Common Multiple (LCM) of 115 and 52
The least common multiple (LCM) of 115 and 52 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 115 and 52?
First, calculate the GCD of 115 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 52 = 2 remainder 11 |
| 2 | 52 ÷ 11 = 4 remainder 8 |
| 3 | 11 ÷ 8 = 1 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 104 | 936 |
| 95 and 153 | 14535 |
| 156 and 95 | 14820 |
| 163 and 107 | 17441 |
| 87 and 20 | 1740 |