Least Common Multiple (LCM) of 45 and 140
The least common multiple (LCM) of 45 and 140 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 45 and 140?
First, calculate the GCD of 45 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 140 = 0 remainder 45 |
| 2 | 140 ÷ 45 = 3 remainder 5 |
| 3 | 45 ÷ 5 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 152 | 6840 |
| 107 and 195 | 20865 |
| 46 and 91 | 4186 |
| 189 and 154 | 4158 |
| 72 and 135 | 1080 |