Least Common Multiple (LCM) of 54 and 145
The least common multiple (LCM) of 54 and 145 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 54 and 145?
First, calculate the GCD of 54 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 145 = 0 remainder 54 |
| 2 | 145 ÷ 54 = 2 remainder 37 |
| 3 | 54 ÷ 37 = 1 remainder 17 |
| 4 | 37 ÷ 17 = 2 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 118 | 6726 |
| 64 and 61 | 3904 |
| 150 and 69 | 3450 |
| 49 and 129 | 6321 |
| 11 and 109 | 1199 |