Least Common Multiple (LCM) of 65 and 58
The least common multiple (LCM) of 65 and 58 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 65 and 58?
First, calculate the GCD of 65 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 58 = 1 remainder 7 |
| 2 | 58 ÷ 7 = 8 remainder 2 |
| 3 | 7 ÷ 2 = 3 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 179 | 3759 |
| 176 and 127 | 22352 |
| 19 and 38 | 38 |
| 158 and 161 | 25438 |
| 60 and 41 | 2460 |