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 |
|---|---|
| 131 and 18 | 2358 |
| 181 and 35 | 6335 |
| 107 and 188 | 20116 |
| 98 and 160 | 7840 |
| 136 and 152 | 2584 |