Least Common Multiple (LCM) of 106 and 30
The least common multiple (LCM) of 106 and 30 is 1590.
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 30?
First, calculate the GCD of 106 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 30 = 3 remainder 16 |
| 2 | 30 ÷ 16 = 1 remainder 14 |
| 3 | 16 ÷ 14 = 1 remainder 2 |
| 4 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 193 | 3860 |
| 194 and 90 | 8730 |
| 141 and 35 | 4935 |
| 123 and 12 | 492 |
| 12 and 105 | 420 |