Least Common Multiple (LCM) of 58 and 109
The least common multiple (LCM) of 58 and 109 is 6322.
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 58 and 109?
First, calculate the GCD of 58 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 109 = 0 remainder 58 |
| 2 | 109 ÷ 58 = 1 remainder 51 |
| 3 | 58 ÷ 51 = 1 remainder 7 |
| 4 | 51 ÷ 7 = 7 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 111 | 5994 |
| 149 and 166 | 24734 |
| 181 and 165 | 29865 |
| 123 and 126 | 5166 |
| 137 and 19 | 2603 |