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 |
|---|---|
| 117 and 85 | 9945 |
| 123 and 127 | 15621 |
| 22 and 59 | 1298 |
| 153 and 88 | 13464 |
| 87 and 184 | 16008 |