Least Common Multiple (LCM) of 35 and 46
The least common multiple (LCM) of 35 and 46 is 1610.
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 46?
First, calculate the GCD of 35 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 46 = 0 remainder 35 |
| 2 | 46 ÷ 35 = 1 remainder 11 |
| 3 | 35 ÷ 11 = 3 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 54 | 1890 |
| 45 and 177 | 2655 |
| 137 and 137 | 137 |
| 34 and 63 | 2142 |
| 137 and 61 | 8357 |