Least Common Multiple (LCM) of 159 and 42
The least common multiple (LCM) of 159 and 42 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 159 and 42?
First, calculate the GCD of 159 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 42 = 3 remainder 33 |
| 2 | 42 ÷ 33 = 1 remainder 9 |
| 3 | 33 ÷ 9 = 3 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 54 | 3510 |
| 152 and 162 | 12312 |
| 59 and 149 | 8791 |
| 13 and 185 | 2405 |
| 60 and 124 | 1860 |