Least Common Multiple (LCM) of 111 and 59
The least common multiple (LCM) of 111 and 59 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 111 and 59?
First, calculate the GCD of 111 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 59 = 1 remainder 52 |
| 2 | 59 ÷ 52 = 1 remainder 7 |
| 3 | 52 ÷ 7 = 7 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 189 | 8694 |
| 19 and 170 | 3230 |
| 196 and 142 | 13916 |
| 19 and 98 | 1862 |
| 64 and 84 | 1344 |