Least Common Multiple (LCM) of 188 and 119
The least common multiple (LCM) of 188 and 119 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 188 and 119?
First, calculate the GCD of 188 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 119 = 1 remainder 69 |
| 2 | 119 ÷ 69 = 1 remainder 50 |
| 3 | 69 ÷ 50 = 1 remainder 19 |
| 4 | 50 ÷ 19 = 2 remainder 12 |
| 5 | 19 ÷ 12 = 1 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 164 | 30668 |
| 188 and 53 | 9964 |
| 16 and 164 | 656 |
| 132 and 20 | 660 |
| 71 and 197 | 13987 |