Least Common Multiple (LCM) of 107 and 54
The least common multiple (LCM) of 107 and 54 is 5778.
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 107 and 54?
First, calculate the GCD of 107 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 54 = 1 remainder 53 |
| 2 | 54 ÷ 53 = 1 remainder 1 |
| 3 | 53 ÷ 1 = 53 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 25 | 275 |
| 62 and 143 | 8866 |
| 58 and 14 | 406 |
| 115 and 85 | 1955 |
| 140 and 97 | 13580 |