Least Common Multiple (LCM) of 49 and 58
The least common multiple (LCM) of 49 and 58 is 2842.
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 49 and 58?
First, calculate the GCD of 49 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 58 = 0 remainder 49 |
| 2 | 58 ÷ 49 = 1 remainder 9 |
| 3 | 49 ÷ 9 = 5 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 21 | 2814 |
| 126 and 163 | 20538 |
| 187 and 135 | 25245 |
| 117 and 189 | 2457 |
| 190 and 101 | 19190 |