Least Common Multiple (LCM) of 55 and 117
The least common multiple (LCM) of 55 and 117 is 6435.
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 117?
First, calculate the GCD of 55 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 117 = 0 remainder 55 |
| 2 | 117 ÷ 55 = 2 remainder 7 |
| 3 | 55 ÷ 7 = 7 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 174 | 4350 |
| 20 and 16 | 80 |
| 194 and 97 | 194 |
| 59 and 37 | 2183 |
| 122 and 128 | 7808 |