Least Common Multiple (LCM) of 58 and 65
The least common multiple (LCM) of 58 and 65 is 3770.
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 58 and 65?
First, calculate the GCD of 58 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 65 = 0 remainder 58 |
| 2 | 65 ÷ 58 = 1 remainder 7 |
| 3 | 58 ÷ 7 = 8 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 29 | 870 |
| 142 and 112 | 7952 |
| 138 and 31 | 4278 |
| 175 and 147 | 3675 |
| 10 and 31 | 310 |