Least Common Multiple (LCM) of 59 and 113
The least common multiple (LCM) of 59 and 113 is 6667.
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 113?
First, calculate the GCD of 59 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 113 = 0 remainder 59 |
| 2 | 113 ÷ 59 = 1 remainder 54 |
| 3 | 59 ÷ 54 = 1 remainder 5 |
| 4 | 54 ÷ 5 = 10 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 68 | 3740 |
| 163 and 79 | 12877 |
| 146 and 127 | 18542 |
| 138 and 92 | 276 |
| 31 and 103 | 3193 |