Least Common Multiple (LCM) of 106 and 58
The least common multiple (LCM) of 106 and 58 is 3074.
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 106 and 58?
First, calculate the GCD of 106 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 58 = 1 remainder 48 |
| 2 | 58 ÷ 48 = 1 remainder 10 |
| 3 | 48 ÷ 10 = 4 remainder 8 |
| 4 | 10 ÷ 8 = 1 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 146 | 20002 |
| 193 and 59 | 11387 |
| 63 and 29 | 1827 |
| 115 and 182 | 20930 |
| 10 and 181 | 1810 |