Least Common Multiple (LCM) of 55 and 113
The least common multiple (LCM) of 55 and 113 is 6215.
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 113?
First, calculate the GCD of 55 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 113 = 0 remainder 55 |
| 2 | 113 ÷ 55 = 2 remainder 3 |
| 3 | 55 ÷ 3 = 18 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 96 | 2976 |
| 108 and 22 | 1188 |
| 61 and 192 | 11712 |
| 49 and 122 | 5978 |
| 145 and 91 | 13195 |