Least Common Multiple (LCM) of 159 and 178
The least common multiple (LCM) of 159 and 178 is 28302.
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 178?
First, calculate the GCD of 159 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 178 = 0 remainder 159 |
| 2 | 178 ÷ 159 = 1 remainder 19 |
| 3 | 159 ÷ 19 = 8 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 136 | 14824 |
| 65 and 23 | 1495 |
| 77 and 17 | 1309 |
| 195 and 128 | 24960 |
| 136 and 69 | 9384 |