Least Common Multiple (LCM) of 145 and 54
The least common multiple (LCM) of 145 and 54 is 7830.
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 145 and 54?
First, calculate the GCD of 145 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 54 = 2 remainder 37 |
| 2 | 54 ÷ 37 = 1 remainder 17 |
| 3 | 37 ÷ 17 = 2 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 56 | 2968 |
| 143 and 38 | 5434 |
| 100 and 86 | 4300 |
| 43 and 103 | 4429 |
| 174 and 99 | 5742 |