Least Common Multiple (LCM) of 54 and 138
The least common multiple (LCM) of 54 and 138 is 1242.
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 138?
First, calculate the GCD of 54 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 138 = 0 remainder 54 |
| 2 | 138 ÷ 54 = 2 remainder 30 |
| 3 | 54 ÷ 30 = 1 remainder 24 |
| 4 | 30 ÷ 24 = 1 remainder 6 |
| 5 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 73 | 876 |
| 170 and 95 | 3230 |
| 154 and 123 | 18942 |
| 25 and 129 | 3225 |
| 112 and 190 | 10640 |