Least Common Multiple (LCM) of 54 and 35
The least common multiple (LCM) of 54 and 35 is 1890.
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 35?
First, calculate the GCD of 54 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 35 = 1 remainder 19 |
| 2 | 35 ÷ 19 = 1 remainder 16 |
| 3 | 19 ÷ 16 = 1 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 160 | 11680 |
| 199 and 32 | 6368 |
| 20 and 10 | 20 |
| 116 and 17 | 1972 |
| 199 and 94 | 18706 |