Least Common Multiple (LCM) of 59 and 116
The least common multiple (LCM) of 59 and 116 is 6844.
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 116?
First, calculate the GCD of 59 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 116 = 0 remainder 59 |
| 2 | 116 ÷ 59 = 1 remainder 57 |
| 3 | 59 ÷ 57 = 1 remainder 2 |
| 4 | 57 ÷ 2 = 28 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 156 | 13260 |
| 108 and 173 | 18684 |
| 100 and 34 | 1700 |
| 132 and 100 | 3300 |
| 141 and 165 | 7755 |