Least Common Multiple (LCM) of 54 and 119
The least common multiple (LCM) of 54 and 119 is 6426.
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 119?
First, calculate the GCD of 54 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 119 = 0 remainder 54 |
| 2 | 119 ÷ 54 = 2 remainder 11 |
| 3 | 54 ÷ 11 = 4 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 64 | 8640 |
| 162 and 45 | 810 |
| 87 and 82 | 7134 |
| 174 and 105 | 6090 |
| 141 and 82 | 11562 |