Least Common Multiple (LCM) of 106 and 54
The least common multiple (LCM) of 106 and 54 is 2862.
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 54?
First, calculate the GCD of 106 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 54 = 1 remainder 52 |
| 2 | 54 ÷ 52 = 1 remainder 2 |
| 3 | 52 ÷ 2 = 26 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 139 | 20155 |
| 163 and 12 | 1956 |
| 159 and 107 | 17013 |
| 120 and 36 | 360 |
| 186 and 189 | 11718 |