Least Common Multiple (LCM) of 115 and 53
The least common multiple (LCM) of 115 and 53 is 6095.
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 53?
First, calculate the GCD of 115 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 53 = 2 remainder 9 |
| 2 | 53 ÷ 9 = 5 remainder 8 |
| 3 | 9 ÷ 8 = 1 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 117 | 1638 |
| 53 and 177 | 9381 |
| 153 and 147 | 7497 |
| 46 and 72 | 1656 |
| 14 and 69 | 966 |