Least Common Multiple (LCM) of 106 and 56
The least common multiple (LCM) of 106 and 56 is 2968.
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 56?
First, calculate the GCD of 106 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 56 = 1 remainder 50 |
| 2 | 56 ÷ 50 = 1 remainder 6 |
| 3 | 50 ÷ 6 = 8 remainder 2 |
| 4 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 170 | 1870 |
| 197 and 131 | 25807 |
| 135 and 73 | 9855 |
| 54 and 103 | 5562 |
| 137 and 161 | 22057 |