Least Common Multiple (LCM) of 140 and 159
The least common multiple (LCM) of 140 and 159 is 22260.
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 140 and 159?
First, calculate the GCD of 140 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 159 = 0 remainder 140 |
| 2 | 159 ÷ 140 = 1 remainder 19 |
| 3 | 140 ÷ 19 = 7 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 |
|---|---|
| 174 and 24 | 696 |
| 199 and 184 | 36616 |
| 162 and 197 | 31914 |
| 70 and 66 | 2310 |
| 83 and 194 | 16102 |