Least Common Multiple (LCM) of 101 and 58
The least common multiple (LCM) of 101 and 58 is 5858.
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 101 and 58?
First, calculate the GCD of 101 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 58 = 1 remainder 43 |
| 2 | 58 ÷ 43 = 1 remainder 15 |
| 3 | 43 ÷ 15 = 2 remainder 13 |
| 4 | 15 ÷ 13 = 1 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 182 | 12922 |
| 38 and 23 | 874 |
| 108 and 97 | 10476 |
| 198 and 65 | 12870 |
| 105 and 67 | 7035 |