Least Common Multiple (LCM) of 30 and 107
The least common multiple (LCM) of 30 and 107 is 3210.
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 30 and 107?
First, calculate the GCD of 30 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 107 = 0 remainder 30 |
| 2 | 107 ÷ 30 = 3 remainder 17 |
| 3 | 30 ÷ 17 = 1 remainder 13 |
| 4 | 17 ÷ 13 = 1 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 28 | 1344 |
| 46 and 110 | 2530 |
| 122 and 193 | 23546 |
| 170 and 35 | 1190 |
| 51 and 27 | 459 |