Least Common Multiple (LCM) of 54 and 124
The least common multiple (LCM) of 54 and 124 is 3348.
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 124?
First, calculate the GCD of 54 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 124 = 0 remainder 54 |
| 2 | 124 ÷ 54 = 2 remainder 16 |
| 3 | 54 ÷ 16 = 3 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 138 | 4554 |
| 148 and 24 | 888 |
| 67 and 117 | 7839 |
| 122 and 35 | 4270 |
| 90 and 157 | 14130 |