Least Common Multiple (LCM) of 35 and 54
The least common multiple (LCM) of 35 and 54 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 35 and 54?
First, calculate the GCD of 35 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 54 = 0 remainder 35 |
| 2 | 54 ÷ 35 = 1 remainder 19 |
| 3 | 35 ÷ 19 = 1 remainder 16 |
| 4 | 19 ÷ 16 = 1 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 25 | 3025 |
| 170 and 84 | 7140 |
| 159 and 62 | 9858 |
| 80 and 112 | 560 |
| 48 and 85 | 4080 |