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 |
|---|---|
| 166 and 116 | 9628 |
| 49 and 150 | 7350 |
| 145 and 164 | 23780 |
| 56 and 75 | 4200 |
| 60 and 126 | 1260 |