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 |
|---|---|
| 45 and 189 | 945 |
| 15 and 152 | 2280 |
| 134 and 27 | 3618 |
| 14 and 96 | 672 |
| 16 and 81 | 1296 |