Least Common Multiple (LCM) of 45 and 145
The least common multiple (LCM) of 45 and 145 is 1305.
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 145?
First, calculate the GCD of 45 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 145 = 0 remainder 45 |
| 2 | 145 ÷ 45 = 3 remainder 10 |
| 3 | 45 ÷ 10 = 4 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 119 | 1785 |
| 81 and 21 | 567 |
| 172 and 76 | 3268 |
| 144 and 73 | 10512 |
| 41 and 29 | 1189 |