Least Common Multiple (LCM) of 15 and 54
The least common multiple (LCM) of 15 and 54 is 270.
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 15 and 54?
First, calculate the GCD of 15 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 54 = 0 remainder 15 |
| 2 | 54 ÷ 15 = 3 remainder 9 |
| 3 | 15 ÷ 9 = 1 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 85 | 9010 |
| 11 and 108 | 1188 |
| 126 and 78 | 1638 |
| 161 and 45 | 7245 |
| 124 and 64 | 1984 |