Least Common Multiple (LCM) of 114 and 59
The least common multiple (LCM) of 114 and 59 is 6726.
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 114 and 59?
First, calculate the GCD of 114 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 59 = 1 remainder 55 |
| 2 | 59 ÷ 55 = 1 remainder 4 |
| 3 | 55 ÷ 4 = 13 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 103 | 12566 |
| 31 and 196 | 6076 |
| 35 and 11 | 385 |
| 184 and 130 | 11960 |
| 87 and 20 | 1740 |