Least Common Multiple (LCM) of 57 and 69
The least common multiple (LCM) of 57 and 69 is 1311.
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 57 and 69?
First, calculate the GCD of 57 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 69 = 0 remainder 57 |
| 2 | 69 ÷ 57 = 1 remainder 12 |
| 3 | 57 ÷ 12 = 4 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 132 | 4092 |
| 139 and 104 | 14456 |
| 185 and 169 | 31265 |
| 152 and 101 | 15352 |
| 164 and 195 | 31980 |