Least Common Multiple (LCM) of 58 and 63
The least common multiple (LCM) of 58 and 63 is 3654.
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 63?
First, calculate the GCD of 58 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 63 = 0 remainder 58 |
| 2 | 63 ÷ 58 = 1 remainder 5 |
| 3 | 58 ÷ 5 = 11 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 107 | 13803 |
| 132 and 15 | 660 |
| 34 and 32 | 544 |
| 101 and 157 | 15857 |
| 168 and 26 | 2184 |