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 |
|---|---|
| 150 and 116 | 8700 |
| 168 and 20 | 840 |
| 53 and 184 | 9752 |
| 134 and 56 | 3752 |
| 181 and 49 | 8869 |