Least Common Multiple (LCM) of 55 and 78
The least common multiple (LCM) of 55 and 78 is 4290.
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 55 and 78?
First, calculate the GCD of 55 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 78 = 0 remainder 55 |
| 2 | 78 ÷ 55 = 1 remainder 23 |
| 3 | 55 ÷ 23 = 2 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 60 | 1020 |
| 53 and 189 | 10017 |
| 155 and 181 | 28055 |
| 131 and 149 | 19519 |
| 168 and 109 | 18312 |