Least Common Multiple (LCM) of 54 and 69
The least common multiple (LCM) of 54 and 69 is 1242.
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 54 and 69?
First, calculate the GCD of 54 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 69 = 0 remainder 54 |
| 2 | 69 ÷ 54 = 1 remainder 15 |
| 3 | 54 ÷ 15 = 3 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 130 | 1430 |
| 13 and 46 | 598 |
| 136 and 18 | 1224 |
| 42 and 149 | 6258 |
| 13 and 194 | 2522 |