Least Common Multiple (LCM) of 55 and 102
The least common multiple (LCM) of 55 and 102 is 5610.
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 102?
First, calculate the GCD of 55 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 102 = 0 remainder 55 |
| 2 | 102 ÷ 55 = 1 remainder 47 |
| 3 | 55 ÷ 47 = 1 remainder 8 |
| 4 | 47 ÷ 8 = 5 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 59 | 6726 |
| 188 and 133 | 25004 |
| 118 and 187 | 22066 |
| 122 and 77 | 9394 |
| 14 and 25 | 350 |