Least Common Multiple (LCM) of 54 and 130
The least common multiple (LCM) of 54 and 130 is 3510.
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 54 and 130?
First, calculate the GCD of 54 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 130 = 0 remainder 54 |
| 2 | 130 ÷ 54 = 2 remainder 22 |
| 3 | 54 ÷ 22 = 2 remainder 10 |
| 4 | 22 ÷ 10 = 2 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 110 | 7590 |
| 162 and 87 | 4698 |
| 111 and 69 | 2553 |
| 38 and 178 | 3382 |
| 96 and 96 | 96 |