Least Common Multiple (LCM) of 59 and 85
The least common multiple (LCM) of 59 and 85 is 5015.
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 85?
First, calculate the GCD of 59 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 85 = 0 remainder 59 |
| 2 | 85 ÷ 59 = 1 remainder 26 |
| 3 | 59 ÷ 26 = 2 remainder 7 |
| 4 | 26 ÷ 7 = 3 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 74 | 3626 |
| 119 and 45 | 5355 |
| 190 and 113 | 21470 |
| 102 and 111 | 3774 |
| 89 and 153 | 13617 |