Least Common Multiple (LCM) of 58 and 74
The least common multiple (LCM) of 58 and 74 is 2146.
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 74?
First, calculate the GCD of 58 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 74 = 0 remainder 58 |
| 2 | 74 ÷ 58 = 1 remainder 16 |
| 3 | 58 ÷ 16 = 3 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 112 | 6160 |
| 165 and 163 | 26895 |
| 65 and 28 | 1820 |
| 176 and 84 | 3696 |
| 120 and 47 | 5640 |