Least Common Multiple (LCM) of 54 and 142
The least common multiple (LCM) of 54 and 142 is 3834.
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 142?
First, calculate the GCD of 54 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 142 = 0 remainder 54 |
| 2 | 142 ÷ 54 = 2 remainder 34 |
| 3 | 54 ÷ 34 = 1 remainder 20 |
| 4 | 34 ÷ 20 = 1 remainder 14 |
| 5 | 20 ÷ 14 = 1 remainder 6 |
| 6 | 14 ÷ 6 = 2 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 120 | 3480 |
| 97 and 123 | 11931 |
| 60 and 183 | 3660 |
| 42 and 155 | 6510 |
| 64 and 191 | 12224 |