Least Common Multiple (LCM) of 106 and 57
The least common multiple (LCM) of 106 and 57 is 6042.
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 57?
First, calculate the GCD of 106 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 57 = 1 remainder 49 |
| 2 | 57 ÷ 49 = 1 remainder 8 |
| 3 | 49 ÷ 8 = 6 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 175 | 1050 |
| 136 and 161 | 21896 |
| 56 and 157 | 8792 |
| 82 and 83 | 6806 |
| 136 and 106 | 7208 |