Least Common Multiple (LCM) of 54 and 120
The least common multiple (LCM) of 54 and 120 is 1080.
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 120?
First, calculate the GCD of 54 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 120 = 0 remainder 54 |
| 2 | 120 ÷ 54 = 2 remainder 12 |
| 3 | 54 ÷ 12 = 4 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 22 | 3410 |
| 159 and 61 | 9699 |
| 61 and 38 | 2318 |
| 122 and 161 | 19642 |
| 196 and 81 | 15876 |