Least Common Multiple (LCM) of 140 and 165
The least common multiple (LCM) of 140 and 165 is 4620.
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 165?
First, calculate the GCD of 140 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 165 = 0 remainder 140 |
| 2 | 165 ÷ 140 = 1 remainder 25 |
| 3 | 140 ÷ 25 = 5 remainder 15 |
| 4 | 25 ÷ 15 = 1 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 81 | 2025 |
| 162 and 107 | 17334 |
| 176 and 113 | 19888 |
| 61 and 23 | 1403 |
| 65 and 110 | 1430 |