Least Common Multiple (LCM) of 53 and 109
The least common multiple (LCM) of 53 and 109 is 5777.
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 53 and 109?
First, calculate the GCD of 53 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 109 = 0 remainder 53 |
| 2 | 109 ÷ 53 = 2 remainder 3 |
| 3 | 53 ÷ 3 = 17 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 131 | 24497 |
| 73 and 130 | 9490 |
| 123 and 105 | 4305 |
| 81 and 74 | 5994 |
| 185 and 44 | 8140 |