Least Common Multiple (LCM) of 119 and 188
The least common multiple (LCM) of 119 and 188 is 22372.
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 188?
First, calculate the GCD of 119 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 188 = 0 remainder 119 |
| 2 | 188 ÷ 119 = 1 remainder 69 |
| 3 | 119 ÷ 69 = 1 remainder 50 |
| 4 | 69 ÷ 50 = 1 remainder 19 |
| 5 | 50 ÷ 19 = 2 remainder 12 |
| 6 | 19 ÷ 12 = 1 remainder 7 |
| 7 | 12 ÷ 7 = 1 remainder 5 |
| 8 | 7 ÷ 5 = 1 remainder 2 |
| 9 | 5 ÷ 2 = 2 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 119 | 357 |
| 12 and 86 | 516 |
| 189 and 77 | 2079 |
| 85 and 130 | 2210 |
| 101 and 180 | 18180 |