Least Common Multiple (LCM) of 13 and 59
The least common multiple (LCM) of 13 and 59 is 767.
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 59?
First, calculate the GCD of 13 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 59 = 0 remainder 13 |
| 2 | 59 ÷ 13 = 4 remainder 7 |
| 3 | 13 ÷ 7 = 1 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 32 | 192 |
| 58 and 27 | 1566 |
| 30 and 48 | 240 |
| 195 and 49 | 9555 |
| 129 and 138 | 5934 |