Least Common Multiple (LCM) of 59 and 111
The least common multiple (LCM) of 59 and 111 is 6549.
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 111?
First, calculate the GCD of 59 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 111 = 0 remainder 59 |
| 2 | 111 ÷ 59 = 1 remainder 52 |
| 3 | 59 ÷ 52 = 1 remainder 7 |
| 4 | 52 ÷ 7 = 7 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 45 | 8145 |
| 183 and 106 | 19398 |
| 46 and 23 | 46 |
| 196 and 22 | 2156 |
| 125 and 117 | 14625 |