Least Common Multiple (LCM) of 13 and 58
The least common multiple (LCM) of 13 and 58 is 754.
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 58?
First, calculate the GCD of 13 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 58 = 0 remainder 13 |
| 2 | 58 ÷ 13 = 4 remainder 6 |
| 3 | 13 ÷ 6 = 2 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 38 | 2698 |
| 142 and 126 | 8946 |
| 94 and 159 | 14946 |
| 138 and 64 | 4416 |
| 107 and 148 | 15836 |