Least Common Multiple (LCM) of 104 and 59
The least common multiple (LCM) of 104 and 59 is 6136.
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 104 and 59?
First, calculate the GCD of 104 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 59 = 1 remainder 45 |
| 2 | 59 ÷ 45 = 1 remainder 14 |
| 3 | 45 ÷ 14 = 3 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 38 | 342 |
| 139 and 25 | 3475 |
| 165 and 155 | 5115 |
| 64 and 115 | 7360 |
| 12 and 190 | 1140 |