Least Common Multiple (LCM) of 54 and 34
The least common multiple (LCM) of 54 and 34 is 918.
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 34?
First, calculate the GCD of 54 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 34 = 1 remainder 20 |
| 2 | 34 ÷ 20 = 1 remainder 14 |
| 3 | 20 ÷ 14 = 1 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 198 | 3960 |
| 140 and 17 | 2380 |
| 71 and 16 | 1136 |
| 109 and 124 | 13516 |
| 175 and 121 | 21175 |