Least Common Multiple (LCM) of 58 and 36
The least common multiple (LCM) of 58 and 36 is 1044.
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 36?
First, calculate the GCD of 58 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 36 = 1 remainder 22 |
| 2 | 36 ÷ 22 = 1 remainder 14 |
| 3 | 22 ÷ 14 = 1 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 128 | 4224 |
| 133 and 77 | 1463 |
| 190 and 110 | 2090 |
| 101 and 164 | 16564 |
| 171 and 174 | 9918 |