Least Common Multiple (LCM) of 54 and 140
The least common multiple (LCM) of 54 and 140 is 3780.
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 140?
First, calculate the GCD of 54 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 140 = 0 remainder 54 |
| 2 | 140 ÷ 54 = 2 remainder 32 |
| 3 | 54 ÷ 32 = 1 remainder 22 |
| 4 | 32 ÷ 22 = 1 remainder 10 |
| 5 | 22 ÷ 10 = 2 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 95 | 9880 |
| 98 and 86 | 4214 |
| 112 and 159 | 17808 |
| 50 and 41 | 2050 |
| 187 and 80 | 14960 |