Least Common Multiple (LCM) of 54 and 115
The least common multiple (LCM) of 54 and 115 is 6210.
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 54 and 115?
First, calculate the GCD of 54 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 115 = 0 remainder 54 |
| 2 | 115 ÷ 54 = 2 remainder 7 |
| 3 | 54 ÷ 7 = 7 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 144 | 2736 |
| 166 and 186 | 15438 |
| 161 and 184 | 1288 |
| 152 and 140 | 5320 |
| 172 and 65 | 11180 |