Least Common Multiple (LCM) of 84 and 159
The least common multiple (LCM) of 84 and 159 is 4452.
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 84 and 159?
First, calculate the GCD of 84 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 159 = 0 remainder 84 |
| 2 | 159 ÷ 84 = 1 remainder 75 |
| 3 | 84 ÷ 75 = 1 remainder 9 |
| 4 | 75 ÷ 9 = 8 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 120 | 20280 |
| 134 and 108 | 7236 |
| 53 and 179 | 9487 |
| 131 and 79 | 10349 |
| 190 and 10 | 190 |