Least Common Multiple (LCM) of 58 and 38
The least common multiple (LCM) of 58 and 38 is 1102.
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 38?
First, calculate the GCD of 58 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 38 = 1 remainder 20 |
| 2 | 38 ÷ 20 = 1 remainder 18 |
| 3 | 20 ÷ 18 = 1 remainder 2 |
| 4 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 142 | 7810 |
| 103 and 20 | 2060 |
| 65 and 56 | 3640 |
| 120 and 87 | 3480 |
| 41 and 36 | 1476 |