Least Common Multiple (LCM) of 18 and 106
The least common multiple (LCM) of 18 and 106 is 954.
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 18 and 106?
First, calculate the GCD of 18 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 106 = 0 remainder 18 |
| 2 | 106 ÷ 18 = 5 remainder 16 |
| 3 | 18 ÷ 16 = 1 remainder 2 |
| 4 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 17 | 306 |
| 197 and 159 | 31323 |
| 20 and 74 | 740 |
| 21 and 134 | 2814 |
| 134 and 120 | 8040 |