Least Common Multiple (LCM) of 107 and 58
The least common multiple (LCM) of 107 and 58 is 6206.
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 107 and 58?
First, calculate the GCD of 107 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 58 = 1 remainder 49 |
| 2 | 58 ÷ 49 = 1 remainder 9 |
| 3 | 49 ÷ 9 = 5 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 49 | 2695 |
| 102 and 157 | 16014 |
| 132 and 105 | 4620 |
| 144 and 150 | 3600 |
| 118 and 175 | 20650 |