Least Common Multiple (LCM) of 42 and 58
The least common multiple (LCM) of 42 and 58 is 1218.
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 42 and 58?
First, calculate the GCD of 42 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 58 = 0 remainder 42 |
| 2 | 58 ÷ 42 = 1 remainder 16 |
| 3 | 42 ÷ 16 = 2 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 |
|---|---|
| 27 and 21 | 189 |
| 183 and 24 | 1464 |
| 69 and 145 | 10005 |
| 67 and 17 | 1139 |
| 26 and 103 | 2678 |