Least Common Multiple (LCM) of 140 and 45
The least common multiple (LCM) of 140 and 45 is 1260.
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 45?
First, calculate the GCD of 140 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 45 = 3 remainder 5 |
| 2 | 45 ÷ 5 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 64 | 8640 |
| 156 and 30 | 780 |
| 179 and 78 | 13962 |
| 107 and 192 | 20544 |
| 55 and 99 | 495 |