Least Common Multiple (LCM) of 59 and 103
The least common multiple (LCM) of 59 and 103 is 6077.
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 59 and 103?
First, calculate the GCD of 59 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 103 = 0 remainder 59 |
| 2 | 103 ÷ 59 = 1 remainder 44 |
| 3 | 59 ÷ 44 = 1 remainder 15 |
| 4 | 44 ÷ 15 = 2 remainder 14 |
| 5 | 15 ÷ 14 = 1 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 57 | 1311 |
| 66 and 90 | 990 |
| 117 and 175 | 20475 |
| 39 and 78 | 78 |
| 155 and 124 | 620 |