Least Common Multiple (LCM) of 55 and 59
The least common multiple (LCM) of 55 and 59 is 3245.
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 55 and 59?
First, calculate the GCD of 55 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 59 = 0 remainder 55 |
| 2 | 59 ÷ 55 = 1 remainder 4 |
| 3 | 55 ÷ 4 = 13 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 85 | 8585 |
| 116 and 157 | 18212 |
| 192 and 85 | 16320 |
| 31 and 83 | 2573 |
| 140 and 97 | 13580 |