Least Common Multiple (LCM) of 188 and 133
The least common multiple (LCM) of 188 and 133 is 25004.
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 133?
First, calculate the GCD of 188 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 133 = 1 remainder 55 |
| 2 | 133 ÷ 55 = 2 remainder 23 |
| 3 | 55 ÷ 23 = 2 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 148 | 3996 |
| 35 and 98 | 490 |
| 110 and 78 | 4290 |
| 20 and 103 | 2060 |
| 190 and 77 | 14630 |