Least Common Multiple (LCM) of 188 and 69
The least common multiple (LCM) of 188 and 69 is 12972.
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 69?
First, calculate the GCD of 188 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 69 = 2 remainder 50 |
| 2 | 69 ÷ 50 = 1 remainder 19 |
| 3 | 50 ÷ 19 = 2 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 114 | 5130 |
| 170 and 170 | 170 |
| 180 and 54 | 540 |
| 194 and 44 | 4268 |
| 157 and 121 | 18997 |