Least Common Multiple (LCM) of 45 and 143
The least common multiple (LCM) of 45 and 143 is 6435.
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 143?
First, calculate the GCD of 45 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 143 = 0 remainder 45 |
| 2 | 143 ÷ 45 = 3 remainder 8 |
| 3 | 45 ÷ 8 = 5 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 69 | 2622 |
| 77 and 61 | 4697 |
| 144 and 44 | 1584 |
| 112 and 152 | 2128 |
| 81 and 154 | 12474 |