Least Common Multiple (LCM) of 55 and 130
The least common multiple (LCM) of 55 and 130 is 1430.
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 130?
First, calculate the GCD of 55 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 130 = 0 remainder 55 |
| 2 | 130 ÷ 55 = 2 remainder 20 |
| 3 | 55 ÷ 20 = 2 remainder 15 |
| 4 | 20 ÷ 15 = 1 remainder 5 |
| 5 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 99 | 16533 |
| 140 and 151 | 21140 |
| 54 and 115 | 6210 |
| 198 and 165 | 990 |
| 188 and 120 | 5640 |