Least Common Multiple (LCM) of 42 and 59
The least common multiple (LCM) of 42 and 59 is 2478.
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 59?
First, calculate the GCD of 42 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 59 = 0 remainder 42 |
| 2 | 59 ÷ 42 = 1 remainder 17 |
| 3 | 42 ÷ 17 = 2 remainder 8 |
| 4 | 17 ÷ 8 = 2 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 178 | 178 |
| 134 and 159 | 21306 |
| 148 and 30 | 2220 |
| 161 and 105 | 2415 |
| 122 and 69 | 8418 |