Least Common Multiple (LCM) of 119 and 180
The least common multiple (LCM) of 119 and 180 is 21420.
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 180?
First, calculate the GCD of 119 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 180 = 0 remainder 119 |
| 2 | 180 ÷ 119 = 1 remainder 61 |
| 3 | 119 ÷ 61 = 1 remainder 58 |
| 4 | 61 ÷ 58 = 1 remainder 3 |
| 5 | 58 ÷ 3 = 19 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 85 | 85 |
| 118 and 97 | 11446 |
| 176 and 113 | 19888 |
| 17 and 140 | 2380 |
| 57 and 52 | 2964 |