Least Common Multiple (LCM) of 69 and 186
The least common multiple (LCM) of 69 and 186 is 4278.
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 69 and 186?
First, calculate the GCD of 69 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 186 = 0 remainder 69 |
| 2 | 186 ÷ 69 = 2 remainder 48 |
| 3 | 69 ÷ 48 = 1 remainder 21 |
| 4 | 48 ÷ 21 = 2 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 110 | 990 |
| 78 and 160 | 6240 |
| 108 and 152 | 4104 |
| 122 and 21 | 2562 |
| 143 and 34 | 4862 |