Least Common Multiple (LCM) of 69 and 57
The least common multiple (LCM) of 69 and 57 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 69 and 57?
First, calculate the GCD of 69 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 57 = 1 remainder 12 |
| 2 | 57 ÷ 12 = 4 remainder 9 |
| 3 | 12 ÷ 9 = 1 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 132 | 2772 |
| 60 and 94 | 2820 |
| 74 and 21 | 1554 |
| 28 and 164 | 1148 |
| 178 and 63 | 11214 |