Least Common Multiple (LCM) of 180 and 119
The least common multiple (LCM) of 180 and 119 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 180 and 119?
First, calculate the GCD of 180 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 119 = 1 remainder 61 |
| 2 | 119 ÷ 61 = 1 remainder 58 |
| 3 | 61 ÷ 58 = 1 remainder 3 |
| 4 | 58 ÷ 3 = 19 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 44 | 6468 |
| 46 and 136 | 3128 |
| 153 and 189 | 3213 |
| 135 and 94 | 12690 |
| 98 and 200 | 9800 |