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 |
|---|---|
| 11 and 111 | 1221 |
| 68 and 44 | 748 |
| 159 and 192 | 10176 |
| 136 and 13 | 1768 |
| 41 and 39 | 1599 |