Least Common Multiple (LCM) of 107 and 30
The least common multiple (LCM) of 107 and 30 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 107 and 30?
First, calculate the GCD of 107 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 30 = 3 remainder 17 |
| 2 | 30 ÷ 17 = 1 remainder 13 |
| 3 | 17 ÷ 13 = 1 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 26 | 1300 |
| 11 and 151 | 1661 |
| 73 and 177 | 12921 |
| 50 and 155 | 1550 |
| 190 and 128 | 12160 |