Least Common Multiple (LCM) of 54 and 143
The least common multiple (LCM) of 54 and 143 is 7722.
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 143?
First, calculate the GCD of 54 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 143 = 0 remainder 54 |
| 2 | 143 ÷ 54 = 2 remainder 35 |
| 3 | 54 ÷ 35 = 1 remainder 19 |
| 4 | 35 ÷ 19 = 1 remainder 16 |
| 5 | 19 ÷ 16 = 1 remainder 3 |
| 6 | 16 ÷ 3 = 5 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 96 | 192 |
| 47 and 34 | 1598 |
| 162 and 190 | 15390 |
| 91 and 190 | 17290 |
| 123 and 98 | 12054 |