Least Common Multiple (LCM) of 111 and 58
The least common multiple (LCM) of 111 and 58 is 6438.
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 58?
First, calculate the GCD of 111 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 58 = 1 remainder 53 |
| 2 | 58 ÷ 53 = 1 remainder 5 |
| 3 | 53 ÷ 5 = 10 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 120 | 840 |
| 83 and 21 | 1743 |
| 103 and 128 | 13184 |
| 158 and 51 | 8058 |
| 130 and 44 | 2860 |