Least Common Multiple (LCM) of 13 and 54
The least common multiple (LCM) of 13 and 54 is 702.
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 13 and 54?
First, calculate the GCD of 13 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 54 = 0 remainder 13 |
| 2 | 54 ÷ 13 = 4 remainder 2 |
| 3 | 13 ÷ 2 = 6 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 69 | 7176 |
| 182 and 108 | 9828 |
| 128 and 118 | 7552 |
| 41 and 30 | 1230 |
| 124 and 86 | 5332 |