Least Common Multiple (LCM) of 67 and 58
The least common multiple (LCM) of 67 and 58 is 3886.
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 67 and 58?
First, calculate the GCD of 67 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 58 = 1 remainder 9 |
| 2 | 58 ÷ 9 = 6 remainder 4 |
| 3 | 9 ÷ 4 = 2 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 61 | 10553 |
| 114 and 45 | 1710 |
| 16 and 106 | 848 |
| 196 and 12 | 588 |
| 173 and 97 | 16781 |