Least Common Multiple (LCM) of 119 and 30
The least common multiple (LCM) of 119 and 30 is 3570.
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 119 and 30?
First, calculate the GCD of 119 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 30 = 3 remainder 29 |
| 2 | 30 ÷ 29 = 1 remainder 1 |
| 3 | 29 ÷ 1 = 29 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 54 | 540 |
| 54 and 105 | 1890 |
| 198 and 200 | 19800 |
| 104 and 41 | 4264 |
| 123 and 107 | 13161 |