Least Common Multiple (LCM) of 42 and 159
The least common multiple (LCM) of 42 and 159 is 2226.
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 159?
First, calculate the GCD of 42 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 159 = 0 remainder 42 |
| 2 | 159 ÷ 42 = 3 remainder 33 |
| 3 | 42 ÷ 33 = 1 remainder 9 |
| 4 | 33 ÷ 9 = 3 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 112 | 8176 |
| 194 and 45 | 8730 |
| 127 and 75 | 9525 |
| 77 and 189 | 2079 |
| 24 and 79 | 1896 |